Manage Groups not listing groups
I'm in 5.7.5 on Drupal 7.64 with no issues, I can see a list of all my groups on this screen (Contacts Menu > Manage Groups).

There isn't actually a search button on this screen - I believe its ajax/javascript that powers the search. After you type something in a field and press enter or tab it refreshes the group listing.

Are there any javascript warnings/clashes in your console?