That $5 number is suspicious to me, or perhaps just geographically skewed. In early 90s, I went to the store and bought cigarettes for my mom almost daily and I remember it being about $2.
Edit: in the link below you can see that over the course of 1990, cigarette prices rose from $35 to $48/carton (so $4.80/pack if you bought them by the carton) in 1990. They were, of course, more expensive if you bought individual packs, or if you lived in the north.
https://otru.org/wp-content/uploads/2012/06/update_may2002.p...