Earth people keep time with three natural heavenly cycles: the day, the month, and the year. Each is important. The day influences short-term rest and activity periods. The month determines the tides and strongly influences medium-term biological cycles in many species (nobody is quite sure how, but it's probably by illuminating the nighttime). The year measures not so much the background stars as the seasons, which influence growing cycles, hibernation, etc.
Your planet orbiting a gas giant will enjoy the same three heavenly cycles as Earth, with the giant taking the place of our nearby moon.
Your planet will probably receive practically all of its radiant input from the giant's sun, with a tiny portion of infrared from the giant, so the day/night influence will be similar to Earth. Of course solar eclipses will be more common and the longest could last several days.
The effect of your monthly cycle will be much more pronounced than on Earth, with that huge giant lighting up the night for almost half the month. Life will have no trouble synchronizing its medium-term cycles, such as estrus, with such a strong natural cue. Sentient females there will be much easier to live with than Earth women. You'll still have spring tides and neap tides, with spring tides at new giant and full giant and neap tides at the first and last quarters, but all tides will be much higher.
However, if you planet is tidally locked to the gas giant, then life is quite different. The day and the month are the same. On the giant-facing side, the nights are never very dark, with a sort of brightness peak as the giant passes through its full phase. The only tides will be those caused by the sun, so their magnitude will be about equal to the difference between spring and neap tides on Earth.
Your annual seasons will depend on either or both the eccentricity of the gas giant's orbit around its sun, and the axial tilt of your planet. The axial tilt of the giant, the eccentricity of your planet's orbit, and inclination of your orbit will not contribute to the seasons.
There is no compelling reason why your seasons should be any different than those of Earth, even if your planet is tidally locked to the gas giant. You can make seasons more or less pronounced by declaring the orbital eccentricity and axial tilt. It's your story and it's your planet.
The four other planets orbiting the gas giant would certainly be visible in the sky, but they would not compel attention the way Earth's moon does, or the way visible rings would. They would be more apparent than the five classical planets are from Earth, being so much closer, but I can't see how they would be prominent enough to add cycles to the main calendar. The main guiding periods for the inhabitants will remain the day, month, and year.
The magical calendar cycles will be overlaid onto the main calendar. They will be calculated and consulted by magic practitioners. They will be largely ignored by the laiety during their ordinary activities, which revolve around farming, sailing, mating, hunting, gathering, and celebrating the results of the foregoing.