I'm trying to figure out what size variable contrast filter i need for the above enlarger in the filter holder above the negative carrier. From what I measured the filter holder, my measurement came out 5 1/2 x 5 1/2, If this is the case then would i need to buy 6x6 filters and cut them down to fit?

yep

Your measurement were correct. I cut down the 6X6 filters to fit. The 23CII used to come with a clear plastic sheet about 3/16 inches thick that fit in the filter drawer. It's a handy accessory. You can rest the filters on top of it, and they are much easier to change.