I use a 60" land pride behind my B7100. It has 16 hp with 13 (I think) to the pto. My tractor runs it just fine. When I cut the field behind the house sometimes the grass is 2 - 3 feet tall. That will bog down my tractor but normal lawn grass cutting 16 horse power is plenty.
I run a Woods RM59- a 5' finish mower- all day long with my B7100, also. I just mowed grass as high as the hood last week- I kept the deck up about 6 inches, took the stalks down, then lowered it on the second pass and kept chopping it up. Absolutely no lack of power, and that was a lot of material. I will post a photo- it was a yard at an ramshackle house that hasn't been mowed in 4 years. A 13 pto hp tractor can run a 60" finish mower, and I wouldn't do it if I was overloading or damaging my tractor.
You need to check a couple of things- do the deck spindles turn freely (if not, you may have bound up bearings or debris around the lower shafts), do the idler pulleys turn freely, is the mower set too low, etc. Your tractor should be able to pull it. It may not mow in thick, fine grass while keeping the RPM's way up, but it should power it satisfactorily.
I used to mow with a Wheelhorse 520H- a powerful Onan 20 hp tractor with a 48" deck. My 13 pto Kubota with a 59" finish mower will mow circles around it, at 3/4 throttle, on half or better the fuel. No lie or exageration.
The grass in that yard was deep enough that deer had been bedding down all over the yard, and you wouldn't have seen them until you walked up on them. I mowed it 4 times to get it down as it is in the photo (chopping it up again and again), and then brushcut the bank on the right up to the tree line. If you look closely at the photo, you can see the growth that we hadn't cleared yet on the right side of the house, and the brambles/trash growth at the end of the tall shrubbery on the left- that's part of the creekbank. The woman who owns it hires someone about every 4 years or so to come in and clean up all the undergrowth. We (two of us) spent 6 days there cleaning the yard and around the house, a section of woods, and about 500' of creek bank. I mowed the yard numerous times, then mowed the sides of the creek bank once cleared.
I say all of this to make a point- my B7100 runs a 59" finish mower with power to spare. I have never taxed it yet. Yours should be able to also run a 5' finish mower at some reasonable level.