To answer OP's question, probably some combination of zero turn and rear finish mower. When we first got our 11 acres I mowed the 4 acres of "yard" with a 60" mid-mount on the BX. Cut was very nice, but it was time consuming and frankly my back usually was killing me by the end of it between the bumps/ruts/general uneveness of the ground and my posture from sitting on a small tractor.
I purchased a 54" zero turn about 6 years back and its been both world's quicker and more comfortable to accomplish on the zero turn, even with the rough terrain (old terraced farm land with clay soils). About the only time I mow with the tractor is to brush hog and that's due either to the zero turn being down or hitting the spots too steep for the zero turn about twice a year.
5 acres may be just about enough to get a neighbor to come and cut and take your hay. Perhaps for free. Especially if you can plant good weed free grass.
Funny you mention the idea of small acreage haying, or at least letting the grass grow. Next door neighbor was like a grandfather to me and always use to gently rib me about growing hay when I let the yard get too long. I'd respect his wishes and break out the mower and get it cut, usually with a follow up comment from him the next day as to whether I needed to borrow a tedder.
He passed about 6 months back and this last week I finally decided I was going let about an acre of my yard grow to see what develops with the idea of slowly managing that section into a wildlife food plot, native grass/forbes patch (lots of wildlife in the neighborhood - deer/turkey/rabbit/fox/flying squirrels/birds/etc).
There's a slope on the backside of my property, next to my shop that I've only ever mowed about twice a year due to the steepness and it consistently has grown a healthy, dominant stand of little bluestem. I'm hoping with some gentle coaxing (maybe some burning, a little herbicide and potentially some seeding) I can get the acre I am letting run wild come up in little bluestem or something similar for both aesthetic and wildlife purposes. With my oldest getting his driver's license, girls and getting further into playing in competition marching band I somehow doubt his interest in running the zero turn will stay as high. It'd be nice to cut down on the amount we have to mow on a weekly basis.