Most people would over train on the program you wrote. Remember that when you train with weights, you are actually breaking down the muscles. It's when you rest/recover that your body actually repairs and grows.
I would do push, pull, legs, rest. I wouldn't train 5 days in a row without a day off. After training hard for 2-3 days in a row, your central nervous system will need a break.
If you can only train M-F, I would do MT, wednesday off, TF, Saturday sunday off