well your 5 rep max would be more than you can handle for 5 sets, 5rm would be 5rm, you could probobly only do 1-3 sets of that, not 5.
But ill stop nipticking and answer the question. I wouldnt count it, if your too tiered to do them right after eacother and have to rest you cant do it. Resting a bit before pulling up again is ok though, it prevents the whole bouncing the weight off the floor thing, i always put the bar down on the floor, so the entire weight rests on the floor, then pull it back up.