I don't know about a cougar, but when I was a kid, I have seen with my own eyes our small herd of Angus cattle chase and run completely off our place a pair of coyotes. Those 'yotes were running for their lives, and I can tell you that our Angus can run a heck of a lot faster than 5mph. The cattle were hot on the heels of the 'yotes and they were getting the "heck out of Dodge"
Of course these cattle were the same ones that would stomp a groundhog hole shut and when he would dig back out they would chase them off the place too and stomp the hole shut again. Those Angus are tough SOB's. When we had mixed breed cattle they never exhibited that kind of behavior. At least not that I ever saw.