5 days is fine if you like hiking very aggresive-but I can say that in our group’s hike of it, doing it in 7 nights and 8 days was hard (and we are all hard core hikers!). I would NOT recomend that it is done in 5 days!!
Thing is, the WT is very pretty-and it needs to be savored. 8 - 10 days is perfect for it. Also, getting your campsites to work out for 5 days isn’t so easy-especially if you want to stay at Indian Bar and you cannot get it.
Our schedule:
Longmire to Nickel Creek.
Nickel Creek to Summerland (I wish we had stayed at Indian Bar! It is the prettiest site.)
Summerland to Sunrise (youch…that was a long day as the White River bridge was out, and we had to road walk to to reconnect)
Sunrise to Mystic
Mystic to Eagles Roost (via Spray and Seattle Parks)
E. Roost to the lakes
the lakes to Puyallup.
The last day hike was a looong one-not the distance persay, but the never ending up and down.
If a person isn’t used to the up and down, I don’t recomend 18 mile days. 9-10 is great. Even then, we never saw under 11 miles.
That and gets dang hot up there in August-you have to plan time to lay in streams midday 
And there are so many side trails to explore and wander! By the time you get done, you can easily do 100-110 miles.
Some people have layday overs so they can go explore. I recomend that if you haven’t been to Rainier before! For instance, if you take the traditional WT and go via Ispuit Pass, a side trip to Eunice Lake is worth it, and up to Tolmie Peak
Or going up to Auroa Lake and beyond. Or walking up to Paradise via Mazama Ridge and the High Lakes Trail.
Mail drops though are very easy-and it gives you a perk knowing that you have some goodies waiting you halfway 
sarbar