There were twenty-seven # 1 songs in 1965. None of the songs listed below were one of them.
There were several songs that reached #2 on the Billboard Hot 100, while many, many others reached the Top 10, and still a few more reached the Top 20.
Below is a medley of 12 songs that may not have hit the top of the charts but each and every one of them is a timeless treasure from 1965. I have indicated below their peak position on the charts next to the artists’ names.

Play button is on the left … Volume slider is on the right

1965 What A Year!

Mamas & Papas (#4) – Gary Lewis & The Playboys (#2)
Kinks (#7) – Sam The Sham & The Pharaohs (#2)
Searchers (#3) – Manfred Mann (#12)
Jewel Akens (#3) – Herman’s Hermits (#2)
Bob Dylan (#2) – Animals (#13)
James Brown (#3) – Jay & The Americans (#4)