Historical clue formulations

• Jack ___, co-founder and longtime C.E.O. of Twitter — 2021-03-11
• Tommy or Jimmy of jazz — 2018-11-04
• Sinatra's big band leader — 2014-09-10
• He signed 5-Down in 1940 — 2013-04-06
• Sinatra employer of the early 40's — 2000-11-07