How do I update Safari on my IPhone 5?

Have you checked Settings>General>Restrictions to see if, perhaps, you disabled it?

See also the instructions for re-installing the preinstalled apps in this article:

Remove built-in Apple apps from the Home screen on your iOS device with iOS 10 - Apple Support

cynthiafrompoplar bluff wrote:

Norton Security is telling me. I'm trying to add my Norton security to my IPhone 5.

That's a bad idea. Norton Security products are one of the surest ways I know of to cause problems on a Mac or iPhone. And there's no reason to use it.

See this article if you're concerned about malware:

Effective defenses against malware and other threats

I am also looking for Safari on my iPhone 5s. I am running OS version 10.3.1 and can't find it anywhere on my phone.

I normally use Google Chrome for my browser, but there is a new app at work that requires Safari if I want to keep getting my work emails sent to my phone. I was able to upload/activate that app on my iPad Air2 without any trouble. Any ideas? Any help will be appreciated!

Versions of Safari on the iPhone are updated with an update of the iOS. If you are using iOS 10.2.1 as indicated, that is the most recent version.

Who is telling you it's out of date?

Norton Security is telling me. I'm trying to add my Norton security to my IPhone 5.

Thanks for the input!