Let's go over the numerous plotholes for a moment
The Genesis Project is a super-secretive affair that is highly dangerous, and yet they only send one ship, The Reliant, out to do the test trials on it.
There are thousands of uninhabited asteroids and planetoids to test Genesis on, yet they need to find a planet hundreds of light years from Earth to do so.
Ceti Alpha V is mistaken for another planet in its solar system that exploded, despite the Reliant having sensors and a computer database which could have revealed that.
A nearby planet exploded close enough to damage its neighboring world, but doesn't end most or all life on that planet?
The Genesis device can be beamed up using a transpoter, but that concept is ignored as a solution in the film's climax.
The Genesis is going to blow up in five minutes, yet somehow the explosion is going to travel at the speed of light or an exceptional fraction of that, because they actually should have had hours or even days for the explosion to have reached them if they were fleeing it at maximum impulse.
The Genesis device can be set to “overload” without any ability to prevent that from happening. Worse, despite the inherent dangers of the device being well-known, Admiral Kirk doesn't seem to have a plan to deal with it.
Everybody seems to have forgotten that both The Enterprise and The Reliant had warp capable shuttlecraft on them which could have carried the Genesis device away from the scene, thus negating the entire premise of the denouement.