Not as such
"Rocky Earth-like planet" - that's your problem right there: a planet five times Jupiter's size cannot be a "rocky Earth-like" one, because it is too large for the light gases to escape during its early life.
So, it will become a gas giant - a huge gas giant. Unless you posit some mechanism to strip it of all light gases, but in that case you're left with a rocky ball with a surface gravity more than 30 times Earth's - no way that's colonizable.
A gas giant has promise though. You can imagine a Saturn-like world, with a very dense core and the rest made up of light elements, so that the "surface" is far enough for the nucleus' gravity to fall off to something a human may survive - no more than twice Earth gravity I'd say. You'll still get Aarn Munro's type inhabitants - squat, probably not very long lived due to heart and circulatory problems. But they'll live long enough.
To provide them a reasonably solid surface, you can imagine very large floating "islands" made up of pseudo-algal analogs, evolved to be buoyant and reach the sunlight.
Okay - 5-J rocky planet it is
Can such a planet exist? Yes. Several improbable but not impossible mechanisms could lead to a light-gases-poor, rocky world that is not also the core of an uninhabitable gas giant.
Plenty of oxygen compounds would be there anyway, and conceivably some organism could start from that and get a breathable atmosphere going, if sunlight can reach the surface (in the case of Saturn and Jupiter, for example, it couldn't).
The significant gravitational collapse could be handwaved away given enough time, or hypothesizing a two-stage planetary formation - first a dense, rocky core, then a substantial cooling off, and finally a Heavy Very Late Bombardment with a new increase in core temperature that doesn't affect the outer layers much. These in turn do not collapse as hard; their kinetic energy is vented off by boiling the initial light gases atmosphere (a young star nearby is needed to supply the necessary massive solar wind). In the end we're left with a fiery ember smothered in silicate dust, nitrogen and water ice, completely airless, but slowly outgassing while the surface gets oxidized. Manage to lose the hydrogen somehow.
We would have a 2-to-3 Jupiter-mass nucleus, say 2.5 (i.e. 800 Earths), with heavy metals, mostly nickel-iron and silicates, and an average density around 15 kg/dm3. This gives us a radius (for the nucleus) of 42380 km. The next 2,5 J-masses form a shell with a lower density - say around 4, even if it's mostly light silicates. Gravity at the shell boundary is around 18 G, and pressure is enough to squeeze them to a higher density.
The "mantle" holds other 800 Earth-masses worth of relatively low-density silicates, and has a thickness of around 28880 km. Surface density is around 2.5, but this way the total planetary radius increases to a whopping 72300 km. This gives us a surface gravity of "only" 6.5 G. Especially in the seas, life is more than possible.
Pressure can be as low as we want (just remove atmospheric gases), the gravity well is deep enough that we needn't fear losing atmosphere. Actually, the problem will be losing enough atmosphere so that what remains is more like air and less like dense soup.
Human life might be possible with some geneering; see this answer and its attached tables. Reasonably long-term survivability of up to 4 G for unmodified humans is also demonstrated by life expectancy of unhealthy, morbidly obese people with body mass up to three-four times normal; it's conceivable that healthy humans could fare no worse, and probably much better. Add some gene splicing from giraffes and humpback whales for adaptations to abrupt pressure changes and blood circulation improvement, remember that people managed to thrive with life expectancies as low as 35 years, and the planet is indeed colonizable.
The planet's surface would be around 125 times larger than Earth's.
A planetary rotation time of 24 hours would lead to a surface speed eleven times Earth's; this would have a marked effect on weather patterns. I haven't calculated the centrifugal effect on gravity, but it would be proportionally higher than Earth's.
Escape velocity might be unattainable with ordinary rockets, which might be impractical (again, I haven't done the math).