Our website is hosted on Drupal 7 but is tied to our database in civi 5.14. We are experiencing a surge in new registrations which require people to fill out a full page of information that then gets tied into our database. This is causing massive delays on our site. How can we optimize civi to improve the speed of our site or reduce the strain?
You're on an insecure version of CiviCRM, you'll want to update it.
Page caching is not going to help, because form interaction is not (page) cached.
I'll assume you've got the usual production caching on, but if you don't, then start there.
If your site is otherwise reasonably responsive, your server is probably running out of resources, either cpu or RAM. You may be on a customized service that has implicit limits the number of concurrent connections (e.g. limiting the number of apache processes/children), or (more likely) you've hit a memory limit and your application is swapping memory to disk.
If you have no way of changing the server or operating system parameters, there's probably not much you can do.
In general, the best way to increase your form interactivity behaviour is going to be using some kind of RAM-based caching (Redis or Memcache), but that's a server thing, not something you can setup purely within Drupal or CiviCRM.