well... I'm glad I didn't reply yesterday... I missed the little cf, & would have commented, that I don't have much interest in rim fire cartridges with as goofy & unpredictable as the market is lately...
as to doing the conversion... I have a buddy that machines bases for the barrels for Contenders, so a regular threaded barrel can be screwed in... so I have many, many custom barrels... one of my latest was a 22 MCF which was loosely based on the old velo-dog center fire 22, & the 22 Cooper CFM... cases for the oddballs can be trouble, it was quite costly to have 100 centerfire 22 cases made, & my buddy was able to make the dies for me...
you would need a reamer, cases, & loading dies... if you are really willing the investment, should be easy enough to do... personally one of the barrels I had made up was for the 17 Mach 2, & I'm quite happy with that...
is there a reason you are sold on the 5mm ???
myself, I've been on a quest to have a couple of the lowest power reloadable cartridge guns... & for the longest time, I was trying to find a .251" barrel to make a "real" gun that shoots 25 ACP... my latest uses a .257 barrel, & shortened 22 Hornet cases to make a 257 "special" ... I have both a Contender barrel in that caliber, & a Ruger Single 10, converted to centerfire, & made into an 8 shot 257 special...