Chosen Solution
The current version of my iPhone 5 is iOS 8.3 after I reset my iPhone 5 it got stuck on the Apple symbol and progress bar, if my uncle updated by computer will it restore all the data without erasing it because I never got to update my iPhone to iOS 9 or 10
You can’t restore your iPhone 5 to iOs 8 since that iOs version is not signed by Apple anymore. You’ll have to settle for iOs 10.
Upgrading your iOS shouldn’t loose your data. In any case you should always backup your phone or any computer! Just in case your phone sprout legs and runs off ;-} How about just backing it up to the iCloud? You have 5 GB free! More than enough to save your phones contents. That way you’re sure not to loose anything.