I think it depends (of course). How much time will you have between Hood and Rainier? How quickly will you recover from a 5000′ climb? Conditions are really variable. During the prime season, there are a lot of people on the hill, the going is slow, and rockfall is an issue. Climbing Hood can be hard or really hard and it is a technical climb not a hike.
As an aside, as I am just on this side of 64, I’d love to hear more about your Rainier plan. My end goal is to climb Rainier and Hood but not this year, as I am focusing on basic training and summit hikes like South Sister.