First, a lot of reasons why this won't work in our universe. Then, an interesting solution. Finally, why the exercise is pointless.
5.0x1030 meters is about 10,000 times larger than the observable universe. That doesn't mean it's larger than the universe, but it does mean that an event on one point of the planet has only had enough time to reach 1/10,000th of the rest of the planet. There has not been enough time in the whole universe for light (and thus anything) to go from one side of the planet to the other. This means there hasn't been enough time for gravity to form it into a sphere, the gravity from one side has not had time to affect the other. One has to wonder how this planet formed in the first place.
Either your universe is very, very, very, very much older than ours, or causality (ie. the speed of light) propagates much, much, much, much faster. Both of these have serious consequences. All sorts of important equations depend on the speed of light, so I'd leave that alone. Make your universe tremendously old. At least 1015 years.
Then there's the question of where this planet is getting its light and heat from? A scaled up star would require an even older universe to be given time to form. Then that requires that your planet rotates. With a circumference of 3.14x1031m, even the smallest rotation will have the surface dwellers moving at the speed of light. There's no way to have anything like a normal day/night cycle, even light will take 1023 seconds to get around the surface. One side bakes, the other side freezes.
An alternative heat source would be better. Our universe has no edge, but perhaps your universe does and it produces light and heat as it gobbles up whatever is "outside". Your planet is in the center of the universe and the surrounding edge is like being inside a spherical heat lamp. Your planet would be in perpetual daytime.
Be careful not to cook the planet by adding to the overall energy of your universe.
Then there's gravity. @Philipp already covered that well, can it be solved? One solution is to mess with the gravitational constant. This will severely alter the makeup of the universe on a large scale, but I'd say that's already happened.
How much smaller should G be? We'll solve g = Gm/r2 for G and plug in an Earth g of 9.8 m/s2.
g = Gm/r^2
gr^2 = Gm
gr^2/m = G
Plug in your numbers... r = 5x10^30 m, m = 2.89×10^96 kg from @Philipp, g = 9.8 m/s^2. We get a G of 8.4x10^-35 N⋅m^2/kg^2 which is 24 orders of magnitude lower than in our universe. Gravity is already very weak, in your universe it's all but undetectable.
Such weak gravity would make your planet take even longer to form. It's questionable gravity could ever form a planet given how much stronger all the other forces would be.
An alternative way to solve the gravity problem is to make the planet hollow. This reduces its mass which reduces its surface gravity. The surface gravity of a hollow planet is a bit harder to calculate, so let's move on to the next problem: how did this shell form and how has it not collapsed?
One possible solution is to put a small black hole in the center of the planet. The "edge" of the universe surrounding the planet is the inverted surface of a white hole. In effect, the planet is both outside and inside a black hole. Material falling into the black hole heats as it falls. This heated material comes out the white hole and creates the warm glow in the sky which heats the planet. As the planet is slowly eaten from the inside, a fine rain of material is falling on the surface from the white hole surrounding it.
This is its geological cycle of renewal, matter on the surface is eventually buried and sinks down to be eaten by the black hole. That same matter falls from the white hole which then rains down on the surface to start the cycle again. Like our own geological cycle, this would be unobservably slow to humans.
The surface of the planet is a standing wave in this flow of particles: a cosmic traffic jam.
This allows your planet without altering gravity or the age of the universe. This is an entirely different universe looping forever.
Even this leaves the basic question of why have a planet so large the inhabitants don't even know they're on a sphere? At your scale the planet would not appear to be flat. The horizon would not appear to curve, ships would not sink over the horizon because they could never reach it. There would be no round, orbiting bodies to hint at the shape of the planet because a planet that large with Earth's surface gravity can't hold on to things in orbit.
Your characters would think they live on a flat, infinite plane and there would be little they could do to prove otherwise. Your sphere is so big they could travel in any direction and never have evidence otherwise. Even at the speed of light for 100 years they'd have gone 1018 m or 1/1013 the circumference, not enough to detect a curve.
From a storytelling perspective, what does living on a giant sphere indistinguishable from a flat, infinite plane gain you?
science-basedtag. $\endgroup$ – SJuan76 Mar 24 '16 at 17:53