I have recent experience with this. We did my son's fence a couple months ago - rented a towable like the one shown above. It worked great.
We were doing 4x4 posts in basically sandy soil about 3 1/2 feet deep - 10 inch auger - so not that hard. It took about 5 minutes per hole. We did 22 holes in about 3 hours - and that was with plenty of rest in between holes.
We had two people and it was a workout and it was very hot - 95 degrees that day. I don't think I would've wanted to do that job alone, but given more time I could have.
They gave us an 18 inch extension which we didn't use. It wouldn't have been very hard to go 5 feet deep, but you would have had to dig down 3 1/2 feet, shut the machine off, disconnect the auger while it is in the hole, add the extension and dig another 18 inches and reverse the procedure to get the auger out. That would have probably made each hole 30 minutes instead of 5.
The OP has only 3 holes, that are bigger than we dug and deeper and probably in more difficult soil. Still I would think that's doable with a rental unit in a couple hours.