This is a really tough group of 16 (after kicking out Whitney and Notorious BIG) for me to select 5.
I am going to put my huge fandom of Soundgarden and NIN aside for a moment.
I am not much of a Judas Priest fan, but you cannot deny their contributions and influence in the metal genre, like it or not. So that's one of my five.
Motorhead--another band I am not a huge fan of, and while they did not sell tons of records, their influence in indisputable. Caught them live at a small club in Wilmington, NC in 1991, and they were fantastic. And Lemmy is god. Two.
Thin Lizzy and the Doobie Brothers are long overdue. They are three and four.
Soundgarden is my fifth, if not my first. Listened to Badmotorfinger on my commute this morning. It's a great album from start to finish. Their other albums are solid. It's a shame they had a hiatus. I caught them live before and after the hiatus, and they were much better after the hiatus. Chris Cornell was one of the top 5 rock vocalists of all time. The range and power of his voice is incredible.