A lot more can go wrong with a community of billions of humans than with an isolated starship with frozen embryos traveling the void between the stars, very little is likely to happen during that almost 5000 year dormant cruise.
Ahem. You're saying that on a Trek board.
1) The ship could be struck by a piece of interstellar debris
2) The AI could get bored and start playing with the stored DNA, combining it with spider DNA to create mutant monsters.
3) The ship could be colonized by space spiders, who mate with the mutant human/spider people
4) The ship could be boarded by a Ferengi raiding party, who get eaten by the hybrid spiders
3187) The ship could travel through a wormhole and end up back at Earth, dumping human-Ferengi-Romulan-Horta mutant space spiders with Borg implants and telekinetic power back on Earth.