The question was answered in post #2. Apparently that wasn't good enough so I will answer it again, hopefully with a little more detail. You want THWN, the W stands for wet. Good luck finding straight THWN though, you will be much better off if you look for THHN/THWN or THWN2. I don't know what size you need because you failed to post a picture of the name plate even though it was requested at least two times. #12 would probably be fine, but since it already has #10, go ahead and use that and you will be covered for sure. You also want to use stranded wire. You need a ground wire, which is green. You will also need two hot colors. Those can be any combination of black, red, blue, brown, orange, yellow, pink, or purple, you can use two of the same color if you would like. Do not, under any circumstances, use white or gray.
Also, since it turns out that the 15' run to the AC is not the feed from the panel to the disconnect, but actually an 8' whip from the disconnect to the unit, you can do whatever you like, but I would run a piece of conduit out the bottom of the disconnect, turn a 90° bend towards the unit and when a couple of feet away from it, adapt to flex so you don't have an 8' run of kinked up flex running to it which will look like **** and no matter how pretty you make it now, will look like **** all over again after a few days in the sun. But, it's not my house and I didn't have anything to do with the install so you can do whatever you like. Also, I'm not sure how you came up with the estimation of 15' of wire in post #14. If the whip is exactly 8' long, you will need 8' of wire in it, but you will also need approximately 1' more on each end for make up amounting to about 10' each. Looks to me like you will need 20' of hot conductor and 10' of ground so if you go to Home Depot and have them cut you off a 15' piece of wire, you're gonna have to go back.
You might also have too large of a breaker in place. If someone used the old AC circuit for the mini split it's very likely that the proper sized breaker wasn't installed, but the information needed to determine that was left out. It will require a picture of the name plate and you will also have to disclose the size of the existing breaker in order for anyone to make that determination.
The reason for the question about the 120 volt receptacle is because the NEC requires a 120 volt receptacle within either 15 or 25 feet of the unit, I don't remember which and to be honest, don't care enough to look it up.
How's that?
