You may need to modify your goal…
You see, the United States Mint didn’t make mint sets in 1965 — at least not the type of mint set we’re used to seeing.
In 1965, 1966, and 1967, the United States Mint made special mint sets. Special mint sets (or SMS) contain one coin of each denomination in proof-like condition.
Because mintmarks were not included on U.S. coins during 1965, ’66, and ’67, the 5 coins in these special mint sets are the only ones you’ll need to complete a collection of U.S. coins from those years.
Incidentally, 1965 was the first year of copper-nickel clad coinage in the United States.
A 1965 special mint set is worth $6 to $8.