I would second everything Michael has said, your trip is neither doable safely and those drives would not be enjoyable, quite the opposite. It would be very work like and not a lot of fun to try and make it to SF in 5 days, but 4 days is asking for trouble. If you got there safely you would be too exhausted to enjoy anything other than to catch up on sleep !

I would consider visiting Zion and Yosemite after Denver and on the way to SF, taking 8 to 10 days overall and then after a day or 2 in SF, head home via a different route as suggested by Michael, over . You could head down to I40 and make stops at places such as the Grand canyon, Petrified Forest, Albuquerque, Memphis and so on over a period of 7 days. If you cut down on the long days behind the wheel and break your journey up into manageable portions, you can have a great time !