If they are similarly priced and you do not have a huge investment in the iOS/Apple App Store ecosystem (music, apps, "all my friends are on Facetime", etc), then the Note 4 pretty much beats anything the iPhone 5 (the 6 is another discussion entirely) has to offer hands-down. Larger screen, much newer device, expandable memory, replaceable battery, S-Pen the lot.
The reasons to choose an iPhone 5 over a Note 4 are mostly going to be that you are heavily invested in the App Store, you are reluctant to give up Apple-proprietary communications systems like Facetime, or the Note 4 is just too big for your purposes/preferences. All are perfectly valid reasons.