PADI Open Water takes 4 dives. It's NAUI that can have 5, though one of those can be swapped for a snorkel dive. Open Water referral generally costs around US$225 + sales tax in San Pedro, and for some inexplicable reason is rather cheaper on Caye Caulker. If you want really CHEAP then go to Honduras.
There are three ways to become a PADI OW diver. One is to do everything here, which takes three full days. Another is the "referral" route, under which you do all classroom and confined water skills learning at home, and just do the four dives here. A popular middle ground is to get the manual and other requisite materials and study them at home, then write the "knowledge reviews" or mini-exams in emails to your chosen dive center. They should mark them and send them back with helpful comments (like "try tiddlywinks instead" - no, I jest). Then all you have to do on arrival is the exam, confined water work (less than half a day) and the four dives. The benefit to you is that you still get to do most of the time-consuming work at home and not as part of your precious holiday time, and without the added cost of a formal referral course - the dive center should not charge you extra for doing it this way. The benefit to us is that we still get to do all the basic water work with you, so we can identify your strengths and weaknesses and work to them.