How to enable logging of 500 and 504 errors on CentOS?

Question

Apache HTTP Server

Hello, there is Apache on CentOS and a script that performs work with a large amount of database operations. After about a minute, either a 504 ngnix error or a 500 error appears in the browser. I want to catch and understand because of what it is?
Previously, hosting was used, but there was not enough capacity, we moved to a 4x2300MGHz server, 4GB of RAM. But nothing has changed at all, how to give all the memory to Apache? The server is only for this task.