I want to update iOS 10.3.4

iPhone 5 is upgradable to 10.3.4 which was released by Apple on July 22, 2019 for the iPhone 5 and iPad 4th gen Cellular as a bug fix.

See: https://support.apple.com/en-us/HT201222

Get help with iOS updates

https://support.apple.com/en-us/HT209571

Get help with over-the-air iOS updates

https://support.apple.com/en-us/HT201435

Get help with iOS update and restore errors

https://support.apple.com/en-us/HT204770

That phone cannot update past iOS 10.3.3.

If you have a requirement to go beyond 10.3.3 than you must upgrade to a newer version of the iPhone.