5 Days looping, ok.
I have done the HM to WP point to point in 3 days while in good but not great shape. However, I was very familiar with the area, which allowed me to cut some distance off the trip.
Here's how I'd do it...
Day One...New Army Pass Trailhead to somewhere on Rock Creek. You will have to push. This will be at least a 10 to 12 mile day but it sets up the rest of the trip. The trip down for the pass is all downhill.
Day Two...to Guitar Lake or the Tarns above it.
Day Three...to Mt. Whitney and back to Lower Crabtree Meadow
Day Four...to Lower Soldier Lake.
Day Five...Over Army Pass and out...I hate Cottonwood Pass and only go over it when Army and New Army Passes are not an option. This is another long day and going through Cottonwood Lakes area back to the car is not all downhill. It is sandy and rock n' rolling.
Army Pass should be open by late July or early August.