Around here the 4 ft. fence works well because it keep our pack of dogs on one side and coyotes on the other. I'm not sure if, at night, they vault the fence.
As I understand it, coyotes an easily climb a 4-5 ft fences. I have heard of "coyote rollers" which appear to be effective at preventing canines from climbing a fence; you can Google their website. I think you could make easily make a coyote roller with some fencing wire and the piping of your choice.
Jim