Hank started on baritone saxophone with Ray Charles in 1958. A great example of his bari work can be heard on the legendary recording of David Newman called "Hard Times".
Hank led a band which worked as an opening act for the RC show, and toured and recorded on it's own during the downtime of the RC band. I remember seeing Hank's band live in Philly at the '64 Quaker City Jazz Festival. Lonny Shaw played bari that night, but Leroy Cooper was the regular bari player, David Newman played tenor, and the trumpet was Johnny Coles. I don't remember who played bass and drums, but there was no full time piano player, they were RC's opening act, after all. When piano was needed, Hank played very nice, tasty piano. He also wrote and arranged for his three horn, two rhythm unit.
He had big hit records in the mid '60s. Check out "Lorelei's Lament", "The Peeper", and "Whispering Grass". These were big radio hits back in the day when jazz musicians crossed over into the pop and easy listing part of the dial, and gained wide exposure and hopefully made a little cash.