For anybody to be of real help you have to define what "affordable" means to you. What's your budget for airfare, accommodations and food. I can't imagine how "eating out" in the Caribbean with 5 kids that age (plus the parents) could ever be termed "affordable" but then again, what's affordable for you many not be affordable for me. That's why you it's important to give us a budget.

Tell us also, what type of island experience you are seeking - big island, small island, lush island, arid island.

How long a trip?

What types of activities interest your family members?

With a family of 5 kids consider renting a villa as you'll probably find it more "affordable".

I think the "Mayan Riviera" (Caribbean coast of Mexico) is more economical than any of the actual Caribbean islands.

Are you willing to consider an all-inclusive resort? With that many in your party it may be a more "affordalbe" option.

Mexico is the about the least expensive vacation option compared to most Caribbean destinations. There are several areas in Mexico to choose from and several great AI resorts in all price ranges.

There are those resorts that have kids eat/stay free as well
Just do a google search