Alrs: I have killed Coyotes with a variety of rimfire cartridges including 22 WRF, 22 MRF, 22 Winchester Auto, 22 LR and 17 HMR.
I have never shot a Coyote with the 5mm Remington Magnum.
Yes indeed - I have no doubt with a well placed shot you would bring a Coyote to bag with your 5mm Remington Magnum.
To date I have killed 3 Coyotes with my 17 HMR Rifle - all one shot kills.
I have heard some states only allow "Varmint Hunting" with rimfires or shotguns - is that your situation?
Yes keep the Coyote numbers down and your Deer and Wild Turkey herds will improve.
Hold into the wind
VarmintGuy