My central a.c. had maintenance 2 mo. ago but I recently noticed water on the floor below.?

I found beads of water on the bottom of the handler, not a lot but damp. The coils seem to be running into the pan but on the left side where there isn't a pan, that's where some slight water seems to be coming from. It doesn't do it all day but only, strangely, during the day. The water seems to slip through an opening onto the bottom of the a.c. itself. I've run chlorox and water, vinegar and water, and also drain cleaner from home depot but it still hasn't stopped completely. The outside pipe seems to be dripping. I live in Florida. Could this be normal? My unit is 5 yrs. old.