Error establishing database connection / Error 500

I used to receive an Error establishing database connection once in a while on my website and sometimes it would really crash badly (I couldn’t even log in to the WP Admin).

After switching hosts, I don’t receive this message anymore, but from time to time, some users, not all, receive a 500 Error.

I need to mention that after I moved to a new host, I installed a fresh WP and uploaded old content in new databases.

What can be the cause?

Thank you!