Multiple crimes of moral turpitude is a ground for removal. If the last of five such crimes occurs over five years prior to applying for green card renewal, will the application be denied or accepted?

If they occurred at all DURING the period the green card was issued... its grounds for revokation.

It is on a case by case basis, if the person shows their life has changed, it can be renewed.
What the "crimes" are, you are very vague there, how many was multiple, what evidence and so on.

Depends on how many times, and nature of crimes. Do not attempt to submit renewal with out good immigration attorney.

How does grounds for removal have to do with renewal? If they wanted to revoke it, they would do it whether you renew or not. It doesn't make sense to say, oh, we are revoking your green card just because you applied to renew it.