Get close enough and you can kill a coyote with a baseball bat, but that doesn't make it a good choice for hunting them.
No 5 Turkey shot just doesn't penetrate like heavier shot will. Think about what it does on turkey: very limited penetration on feathers and breast meat (if any), and only kills if it hits exposed skin of the neck and head.
I have been using Winchester Super-X 00 Buckshot for about 20yrs, very hard to beat this load for coyotes.
In the last few years, I've been experimenting with new loads, Hevi-Shot Dead Coyote T shot does very well. The Federal Flight Control No.4 Buck and No.1 buck are also doing very well for me this winter. I'm excited to try the new Winchester Supreme hi-density X-tended Range Coyote B loads, but I'm a bit nervous about the small pellet size.
In general, your rule of thumb can be "use buckshot". There's a big gap between even No4 or 5 turkey loads and Buckshot. The Dead Coyote Hevi-shot gets away with being a smaller shot (T buckshot) because it's heavier than lead.
Copperplated turkey shot will have even less penetration than all lead.
Tried and true 00buckshot with a modified or improved choke is cheap enough that it's hard to reason why anyone would use a sub-par load.