Couple of issues.
Can I transfer my S7E setup to the S5?
I have a Gear S2.... can that transfer to the S5 without reseting the watch?
I'm sure that the watch will be reset no matter what you try to do, it simply doesn't like 1 watch multiple devices setup, really a Pain in the **s for people like me with multiple devices, I just gave up and left it just for when I'm using my S7 edge.
About the setup, I really don't know if Smart Switch (Desktop version) will even recognize the S5, and even if it does, what you normally restore from this backups are mostly pictures and audio files, most of the other settings will likely not being compatible being different App versions. You'll need to just try to see what happens. Next time, before you get rid of the phone, install Smart Switch App on the other phone (or sideline it via an APK download), the S7 and Notes will have it pre-installed, and with both phones on your possession it works good enough to save you some precious time in the process.