How to get rid of over 4500 old emails on my iPad?

Assuming that you are using the native Mail App to access and manage your email, while there isn’t a Select All button for many of the mailboxes, with a few steps it remains possible to bulk select and delete email.

Start by searching your mailbox (or other mailbox folder) by Sender or suitable keyword - and/or combining with a filtered view in the Mail App sidebar:

Flag and filter emails on iPad - Apple Support

Next, tap the Edit button at top-right of the Mail sidebar; simply swipe your finger down (or up) the left-side of the message list to bulk select Mail Messages. Swipe below the bottom edge to rapidly select all the visible email messages.

Once selected, tap the Delete button at the bottom of the sidebar.

Delete them in your AOL account on their website (and off your computer if there are any there).