I am looking at wet dry vacuums and there is one that says 5 HP at 9 amps ;180 watts.... I saw some that claim 1.75 HP, but how can I tell what the real power use is? and there is another "The vac is 3.5 HP and 175 watts" ???? and what is 1.75 Peak HP ? Well of course they don't say the efficiency %..... I have a dry vacuum that says 12 amps , But that seems a lot for off grid use. I have about 300 to 350ft of 10g wire. What is going to burn out the wire?

Pay no attention to the horsepower ratings. It is all marketing BS. Power in Watts is Volts times Amps. That is all you need to know. 350 feet of 10 gauge wire will have a resistance of about .33 ohms. See this table http://www.interfacebus.com/AWG-table-of-different-wire-gauge-resistance.html I know you are off the grid, what voltage are you transmitting on this 300 foot line? 110V, 220V or 12V? Voltage drop in the line is found from Ohms law V= I*R . So the drop in that line is V=.33* I. 10g wire is normally rated at 30Amps from a heating/fire concern. But if that long run is at 12 volts you will need to be concerned about voltage drop. 30 amps would be a 9 volt drop, Insignificant at 220 Volts. and 75% of your available juice at 12 volts.