If your planet has a mass of 7 Jupiters or 2,224.6 Earths, it is easy to calculate the semi-major axes of the orbits of the moons from their orbital periods and their masses.
According to this online calculator,
https://www.omnicalculator.com/physics/orbital-period
Moon 1 with a mass of 0.15 Earth and an orbital period of 24 hours would have an orbit with a semi-major axis of about 551,000 kilometers if if it had an orbital period of about 24.03 hours.
Moon 2 with a mass of 0.3 Earth would have an orbital period of about 36.01 hours with a semi-major axis of about 722,700 kilometers.
Moon 3 with a mass of 0.25 Earth would have an orbital period of about 53.99 hours with a semi-major axis of about 946,700 kilometers.
Moon 4 with a mass of 0.25 Earth would have a orbital period of about 81 hours with a semi-major axis of about 1,240,650 kilometers.
Moon 5 with a mass of 0.15 Earth would have a orbital period of about 122 hours with a semi-major axis of about 1,630,300 kilometers.
You will note that AlexP's comment suggests that an orbital period of 121.5 hours instead of 122 hours would be closer to the geometric progression you use, and Vesper's comment suggests that you make the orbital period of Moon 5 108 hours instead.
The star of the system is said to be an F5V and the planet's orbit has a semi-major axis of about 1.8 AU. A standard F5V star would have a mass of 1.33 mass of the Sun and a luminosity of 3.63 the luminosity of the Sun.
According to this Hill sphere radius calculator:
https://www.vcalc.com/wiki/hill-sphere-radius
The planet's Hill radius should be about 30,377,141.326 kilometers. So the moons should have long term stable orbits as far as the gravity of the star goes. Actually the true long term region of stability only goes to one third or one half of the Hill radius. And in this case it would only be to 10,125,713.77 to 15,188,570.66 kilometers. And the 5 moons would still be well within the limit for long term stability.
If a standard F5V star has a luminosity of 3.63 Suns, the square root of 3.63 is about 1.90256. The distance from the 55V star where the planet would receive as much radiation from the star as Earth gets from the Sun, which I call the Earth Equivalent Distance or EED, should thus be 1.90256 AU.
And your question says that the planet and its moons are within the habitable zone of your star. Are they? The answer is a solid maybe, maybe not.
You will note that at 1.8 AU your planet and its moons are at about 0.946 of the distance to your star's EED and thus should be a bit hotter than Earth.
Here is a link to a table with about a dozen recent estimates of the inner and/or outer edges of the Sun's habitable zone.
https://en.wikipedia.org/wiki/Habitable_zone#Solar_System_estimates
Notice the vast differences in some estimations of the limits of the Sun's habitable zone. The ones which extend the limits far from the Sun or close to the Sun probably involve specific types of atmospheres for the worlds, atmosphere types which might not be suitable for your story.
And notice that 5 estimates of the inner edge of the Sun's habitable zone put it at farther out than 0.946 AU, the equivalent of where you put your planet's orbit.
Those calculations claim that if planet receives slightly more radiation than Earth gets the planet will suffer a runaway greenhouse effect, like Venus, and be unable to have liquid surface water, vital for habitability.
The heat necessary to trigger a world's runaway greenhouse does not all have to come from the radiation of its star. All planets and moons have some internal heating, left over from their formation, and from radioactive decay, and from tidal heating from gravitational interactions with other astronomical objects.
All those interior heat sources have to combined with the heat from the star to ge the total heat at the surface. It is theoretically possible for tidal heating of a world to be sufficient to make an otherwise too cold world warm enough for life, and it is also possible to make a world which would be just right too out and suffer from a runaway greenhouse effect.
In fact, in some cases, tidal heating can be enough to make a world not merely suffer a runaway greenhouse effect, but to become a volcanic hell like Io, a moon of Jupiter.
There have been a number of scientific articles discussing the factors which could influence the potential habitability of hypothetical large exomoons orbiting giant exoplanets.
One is "Exomoon habitability constrained by illumination and tidal heating", Rene Heller and Rory Barnes, 2013.
https://arxiv.org/pdf/1209.5323
This article introduced the concept of a "habitable edge" for giant planets. A moon must orbit outside the "habitable edge" of a giant planet in order to avoid excessive tidal heating and a runaway greenhouse effect.
Heller and Jorge Zuluaga authored "Magnetic shielding of exomoons beyond the habitable edge" 2013.
https://iopscience.iop.org/article/10.1088/2041-8205/776/2/L33/pdf
In it they discussed the formation of planetary magnetic fields and their extension to enclose some of a planet's moons. A planetary magnetic field could subject a moon orbiting in a radiation belt of the planet to high levels of radiation. And it could sometimes also protect a moon without its own magnetic field from cosmic radiation and the stellar wind.
The abstract says:
Moons at distances between about 5 and 20 planetary radii from a giant planet can be habitable from an illumination and tidal heating point of view...
So it seems that 5 planetary radii would be the habitable edge and 20 planetary radii the outer edge of the magnetic field.
If your planet has 1.37 times Jupiter's equatorial radius of 71,492 kilometers, it will have a radius of 97,944.04 kilometers.
Five times that radius will be 489,720.2 kilometers, and twenty times that radius will be 1,958,880.8 kilometers. So apparently moons 1 through 5 will be beyond the habitable edge and also within and shielded by the planet's magnetic field in case they don't have magnetic fields of their own.
You should probably check this article for the formulas used for calculating the Habitable edge of a planet.
https://arxiv.org/pdf/1209.5323
Even though the five moons seems to be beyond the planet's habitable edge and thus safe from excessive tidal heading, they might not be safe from runaway greenhouse effects.
At 1.8 AU your planet and its moons are at about 0.946 of the distance to your star's EED and thus should be a bit hotter than Earth. The amount of radiation they receive from their star should be about one divided by 0.946squared, or one divided by 0.894916, or 1.117423311 times the radiation they would receive at the EED or at Earth's orbit around the Sun.
The solar constant of radiation at 1 AU from the Sun is about 1.361 to 1.362 kilowatts per square meter. So the planet and its moons would receive about 1.520813126 to 1.52193055 kilowatts per square meter.
Because of earth's shape, cycle of day and night, and reflection of light back into space, out of a solar constant of 1.361 to 1.362 kilowatts per square meter, the solar energy at Earth's surface averages about 240 watts per square meter. 1.117423311 times that would be about 268.1815 watts per square meter.
And on page 5 Heller and Barnes say that about 300 watts per square meter would be enough to start a runaway greenhouse effect.
So even if your moons don't suffer runaway greenhouse effects they are likely to be be considerably warmer than Earth.
The Masses of Your Moons.
Your statement that your planet is in the habitable zone indicates that you want the moons to be habitable for at least some forms of liquid water using life. Thus the moons need atmospheres - possibly much less dense than Earth's - to keep water liquid at their temperatures. And if they have liquid surface water they can have microscopic life forms.
And if you want large multicellular plants and animals your moons will have to have relatively dense atmospheres rich in oxygen, so that human beings and other lifeforms with similar requirements can breathe the air.
Most scientific discussions about the potential habitability of other worlds focus on habitability for liquid water using lifeforms in general. The only discussion of the potential habitability of other worlds for human beings (and thus lifeforms with similar requirements) is Habitable Planets for Man Stephen H. Dole, 1964.
https://www.rand.org/content/dam/rand/pubs/commercial_books/2007/RAND_CB179-1.pdf
There are many factors which can speed up atmospheric loss by a world. And probably the most important is the escape velocity (and not the surface gravity) of the world. According to pages 34 & 35, a rule of thumb for how long world can retain 0.368 of the original amount of a gas depends on the ratio of the escape velocity divided by the root-mean-square of the velocity of that gas in the exosphere.
According to table 5 on page 35 the time it takes for the amount of a gas in the atmosphere to go down to 0.368 of the original amount varies between zero time with a ratio of one or two up to infinite time with a ratio of six. A comparatively small change in the ratio makes the difference between instant atmospheric loss and retaining the atmosphere for infinite time.
On page 54 Dole decided that the minimum mass of a planet which could retain oxygen in the atmosphere for long periods of time would be one which an escape velocity of 6.25 kilometers per second, which Dole believed would be a world with 0.195 earth mass, 0.63 Earth radius, and a surface gravity of 0.49 g.
Dole believed that the density of atmosphere a world would produce depended on its mass, and thought that a world would have to be much more massive than 0.195 Earth mass to produce a dense, oxygen rich, atmosphere. Discovery of the dense atmospheres of Venus and Titan shows that the density of a world's atmosphere is not proportional to its mass, and therefore it is possible for a world with a mass as low as 0.195 Earth to produce a dense atmosphere as well as retain it for long periods of time.
Heller and Barnes discuss the mass range of habitable moons on pages 3 and 4.
A minimum mass of an exomoon is required to drive a magnetic shield on a billion-year timescale (Ms ≳ 0.1M⊕,
Tachinami et al. 2011); to sustain a substantial, long-lived atmosphere (Ms ≳ 0.12M⊕, Williams et al. 1997; Kaltenegger
2000); and to drive tectonic activity (Ms ≳ 0.23M⊕, Williams et al. 1997), which is necessary to maintain plate tectonics and
to support the carbon-silicate cycle. Weak internal dynamos have been detected in Mercury and Ganymede (Kivelson et al. 1996; Gurnett et al. 1996), suggesting that satellite masses > 0.25M⊕ will be adequate for considerations of exomoon habitability. This lower limit, however, is not a fixed number. Further sources of energy – such as radiogenic and tidal heating, and the effect of a moon’s composition and structure – can alter our limit in either direction. An upper mass limit is given by the fact that increasing mass leads to high pressures in the moon’s interior, which will increase the mantle viscosity and depress heat transfer throughout the mantle as well as in the core. Above a critical mass, the dynamo is strongly suppressed and becomes too weak to generate a magnetic field or sustain plate tectonics. This maximum mass can be placed around 2M⊕ (Gaidos et al. 2010; Noack & Breuer 2011; Stamenković et al. 2011).
Thus Heller and Barnes conclude that a mass of 0.25 Earth should be enough for a habitable moon. So your Moons 2,3, and 4 should be massive enough to be potentially habitable according to Heller and Barnes, as well as over Dole's limit of 0.195 Earth mass.
Your moons 1 & 5 at 0.15 Earth mass are below Heller and Barnes's 0.25 Earth mass limit and Dole's 0.195 Earth mass limit. But they are above the limit of 1.2 Earth mass for retaining an atmosphere.
I note that the speed of gas particles in the exospheres where gases escape depends on their temperatures in those regions of the atmospheres. And their temperatures in the exospheres depends on the flux of hard ultraviolet radiation in the exospheres. By putting your planet and moons closer than the EED of the star you increase all the radiation they receive from the star including the ultraviolet, by 1.11742331 times. And the hotter temperature of the F5V star you chose means that it will emit a higher proportion of ultraviolet light.
Putting your planet and moons n orbit around a cooler star, maybe a K0V, would reduce their exosphere temperatures and make it more probable for your moons to retain atmospheres.
