How to download Instagram to iOS 10.3.4?

Unfortunately you can't do that.

Instagram requires iOS 11 or later version (see this article https://apps.apple.com/app/instagram/id389801252 , and your iPhone 5, because of hardware incompatibility, cannot support versions beyond 10.3.4.

Regards

Giulio

The iPhone 5 is too old / outdated by now, and it cannot support most apps anymore, since those require atleast iOS 11 by now, and the iPhone 5 cannot be updated past iOS 10.3.4.

Sorry.