It depends on several factors, including the condition of the coin, any mint errors or varieties, and the current market demand.

In 1965, the United States Mint produced both copper-nickel and silver nickels, depending on when they were minted that year. The silver version was produced from late 1964 to early 1965, and contains 35% silver. The copper-nickel version was produced from mid-1965 to the present day.
If your nickel is a silver nickel, it could have some value as a collectible coin. The silver content alone gives it a base value of its silver weight, but it could be worth more depending on the condition and rarity. A worn or damaged silver nickel may only be worth its silver content, while a well-preserved, uncirculated silver nickel with no mint errors or varieties could be worth several dollars to a collector. However, it is important to note that the value of silver can fluctuate based on market demand, so the value of a silver nickel may also vary over time.
If your nickel is a copper-nickel version, it may not have much collectible value beyond its face value of five cents. However, there are a few varieties and mint errors that could increase its value to collectors. For example, some 1965 nickels have a minor die clash error, where the image from one side of the coin is imprinted onto the other side, creating a doubled image. This variety can be worth a few dollars to collectors, depending on the extent of the error and the condition of the coin.
Another possible variety is the “special mint set” nickel, which was produced in 1965 and sold only to collectors. These nickels have a proof-like finish and are in higher condition than regular circulating nickels. They can be worth several dollars to collectors, depending on the condition and whether they are still in their original packaging.
Finally, the condition of the coin can also affect its value. A well-preserved, uncirculated 1965 nickel with no varieties or mint errors may be worth a few dollars to collectors, but a damaged or heavily worn nickel may only be worth its face value of five cents.
It is important to note that the values mentioned here are only estimates and are subject to change based on the current market demand and condition of the coin. If you are interested in determining the value of your 1965 nickel, it is recommended that you consult with a professional coin dealer or appraiser, who can provide a more accurate assessment based on the specific details of your coin.