I'm going to relate my REAL LIVE experience on this subject...
I've owned numerous 22 Win. Mags. over the years, i still do, and i've always liked the round... Way back in the 70's i bought two new 5mm mag's., a Rem. 591 and a 592. I also bought up numerous boxes of ammo for them and scoped them both.
At that time i was hired by a city to clean up some dog problems they were having. I needed the money, and it paid good, so i took the job... I was made animal control officer, and was told "off the record" to get rid of the problem dog packs "how ever i could"... It didn't take long to figure out that i'd need to shoot the dogs to get rid of them, so i did just it.
I tried a lot of different cartridges and rifles, including the 22 Win. Mag, and the 5mm Mag... There's NO question that the 5mm out performed the 22 Win. Mag... It would flatten bigger dogs "quicker", further away than the 22 Mag. would! It's sad that i had to shoot those dogs, but it had to be done, as many were starveing and were abondoned...
I fell in love with the tube feed model 5mm, and still have it to this day. It holds a lot of ammo, and i don't have to worry about loseing a magazine... I still have around 20 boxes of the old Rem. ammo around, and i'll probably buy some new ammo too...
I shot a lot of dogs with a 17 Rem. too, and it was good for longer shots than the rimfires could be used, but for the longest toughest shots i used my trusty .243 Win... I took out over 300 dogs before i had the problem under control, so i did get some experience with all of these rounds... Probably the best thing that happened to me from all of that was, i became a pretty decent running game shot, a running dog at 150 yards was in BIG trouble if i had my 243 in my hands, and i dropped them running further away than that more than a few times...
Compareing the 5mm to todays 22 Mag. ammo, things may be different, but back in the day, the 5mm just kicked the 22 mag's a$$...
DM