Doable, but you need to pick your route
From SF to Seattle in 5 days if very doable, but you will to pick your route to spend a full day in Grant's Pass, and get some sightseeing done.
My opinion is that you have to decide if you want to see the Redwoods, or the Olypmic Pennisula/ National Park region of Washington State, or the Napa/ Sonoma Wine Country, or the Oregon Crater Lake area. Basically its 2 days drive from SF to Seattle by the fastest route (and some longish driving days), plus a full day in Grants Pass so you have 2 days to play with for places to visit.
My guess at your best option would be
Day 1 - SF to Eureka CA area via US 101. This is a (typially) 2-4 lane highways, which winds up through the coastal valleys north of SF, and comes out at the Pacific Coast near Eureka.
Day 2 - Redwoods Parks, then over the Coastal Mountains to Grants Pass. There are several Redwoods parks, including Redwoods National Park, and several California Redwoods State Parks. Continuing up on 101, you'll come along through the Redwoods to Crescent City, CA and from there inland on a 2 lane good quality highway which winds up through the mountains, and over them via Cave Junction to Grants Pass.
Day 3 - Grants Pass.
Day 4 - Through Crater Lake, stay somewhere in Oregon (either back to Eugene OR area, or farther north to Bend)
Day 5 - to Seattle
This gives you Redwoods, some coast, and then mountains before Seattle.