Nice property! 5 acres with a lake is just what I would love to get. I was close awhile back with 2 1/2 acres with a stocked lake adjacent to the property, but some issues came up.
You could look into a ZTR with a rear discharge. But as a few have mentioned with what you plan on doing a tractor with a finish mower would probably serve you well.
John Deere X300 42"
Stihl BR-600 Magnum
AMSOIL In Everything I own