This bank does business in my area, and I was curious as to the odd name.

Turns out the current corporation was formed when two smaller banks merged, in order to have a better shot at making it. During this time period, banks were normally named things like “First National Bank or Podunk”. The larger bank was the 5th national bank, and the smaller bank was the 3rd National Bank. When they combined, they took both names and because the 5th / 3rd National Bank.

https://en.wikipedia.org/wiki/Fifth_Third_Bank