I don't think provenance means much for a mint garnet, since it is all grossular and it's just a lighter version of tsavorite. The value issue is that it is a green shade of grossular and a rather large size. While only about half the value of a similar grass-green tsavorite, it is still worth about $750 to $1000/ct at retail in the sizze you mention. ID would be via RI, single refraction, UV fluorescence (pink) and maybe inclusions. Apparently it also occurs in Madagascar in addition to Merelani (Tanzania) and maybe Mt. Tsavo area in Kenya across the border from Tanzania.
You might try to sell this to jewelry stores or manufacturers who make high end jewelry, or to collectors. You could try ebay or Etsy or consign it to custom cutters who cut this type of stuff. Getting a retail price for this is going to depend on finding someone who collects these stones unmounted and there are not a lot of those people. Otherwise, most of the buyers are going to want to knock a percentage off the retail price of $3200 to $5000 for a five carat stone, since they would be setting the stone in jewelry and then selling it. Say maybe 50 to 75% of retail. You could have this set and sell it, but a stone like this isn't usually set as an unadorned solitaire. You'd probably want some very nice diamond accent stones to go with it and might even want to mount it in platinum in a handmade or custom designed setting, at which point you'd have a good amount of bucks in the mount itself.
You might ask around with high end jewelers and custom cutters and see who might have a list of clients/collectors who look for this kind of thing. Paying a commission to one of these could well lead you to a higher return in the end.