Change your lower unit oil with any good 80wt to 90wt marine grade gear lube of your choice.
Make sure you have new plastic or fiber washer that goes to both the drain plug and the air vent plug above. Those little plastic or fiber washers crack or leak over time. That is why at the end of each season it is recommended to drain the lower unit to evaluate your gear lube to check for water. Also when the lower unit is refilled new plastic or fiber washer are replaced.
After a couple of outings, check your check your gear lube. If it is contaminated with water and looks a little milky then,
crazymanme2 is right, time to check your lower unit seals, drive shaft seals and shift rod seal.
***Check to make sure 2 plastic or fiber washer are not in place. Sometimes they are pushed by the screw plug and aren't seen, so someone will put another one thinking there was no washer to start off with. This can certainly lead to water intrusion into the gear case due to insufficient sealing.
Here is link to digital diagram of your motor. (I assume it is 1964 Evinrude 5.5hp...it was the last year they made the 5.5hp)
https://www.marineengine.com/parts/vintage-evinrude-johnson/278539/catalog.html?https://www.marineengine.com/parts/vintage-evinrude-johnson/278539/27853900001.htm
Here is a diagram and parts list of the lower unit of a 1964 Evinrude 5.5hp (it does not show the washer, but it is there, I promise!!) Item #22 top and bottom plug