The one way, with a hitch or shuttle from the Portal back to HM, is more doable in 5 days: I don't know about an out and back; depends on your capability. But don't give up on walk-in/cancellation permits, especially if you can start on a Sunday through Wednesday. ANd definitely GO: even if you can't get Whitney, there is a lot of great country accessible from Horseshoe, Anvil Camp and Onion Valley that a lot of people find an even better wilderness experience.
