My Samsung s5 on and go off

This sounds like an issue with the motherboard on the phone. Generally speaking problems like this are often a chip level issue where advanced repair is required and is rarely worth fixing, especially if the phone is older.

I'd try and heat up the board to make it functional enough that you can recover the data on the phone and then erase it so you can recycle it. This post was written for my LG G4 (which I no longer use), but the general idea of heating the board up for data recovery applies to all phones: How do I get the phone working for data recovery?. For a phone like this and how hard it is to open I'd probably recommend a minimum of 5-6 minutes of heat to the board. Anything past 8 minutes is probably going to do more harm then good. If you want to get more heat to the chips (and are comfortable doing this) I'd see if you can remove the RF shields non-destructively. Some phones solder it, so this isn't always going to be the case, as was the case in my LG G4. IIRC Samsung shields are usually soldered.

Disassembly of this phone is going to be much more of a pain. To open the phone and remove the motherboard to heat it up, refer to this guide: Samsung Galaxy S5 Motherboard Replacement. Once you have it apart, follow those instructions if you're comfortable doing it and then only assemble enough of the phone that you can easily access the motherboard.