Is it better to evolve them or not to evolve right away?

Depends entirely on the Pokemon.

Does it change the stats depending on evolving it right away as opposed
to evolving it 5 lvls later or just the priority of the moves? (Right now im thinking
of evolving Cyndiquil.

I don't believe stats are effected until it evolves. I don't think there are repercussions for holding it back from evolving either.

You just have to check their moves, and see if it's worth the wait.

For example:

At level 23 Nidorino learns Horn attack, at level 23 Nidoking learns Thrash. Therefore, it's better to wait until level 23 to evolve Nidorino because then you get two moves without sacrificing any others.