Hi Nathalie!
With 5 full days, I recommend visiting all four Walt Disney World theme parks. Your boys will almost certainly enjoy the Magic Kingdom the best. However, all four theme parks are fabulous and you may enjoy one of the other ones more. For example, many adults love Epcot the most. Epcot has a reputation for not being the most child friendly park, but I don't think that's deserved. Both of my boys, now 12 and 7, loved Epcot when they were younger (and they still do); they specifically loved the Future World portion of Epcot. That said, it is true that neither are huge fans of the World Showcase portion of the park, where the country pavilions are located. However, Epcot is so large that you can spend your entire day in Future World and never get bored! I recommend visiting the parks in the following order:
- Epcot
- Disney's Animal Kingdom
- Magic Kingdom
- Hollywood Studios
- Return to your favorite!
It's not black and white; some guests prefer going to the Magic Kingdom first. However, I suggest not doing that because then your boys won't be disappointed when you can't spend every day in that magical place!
With regards to the weather, it will be warm but hopefully not too humid. However, I have been there in May when it is very hot and humid. Definitely bring your swimsuits! In fact, you may want to just spend a day at your resort and relax by the pool. I know my boys loved that when they were younger; in fact, they still do!
If you are staying in a Disney owned and operated hotel then parking is free at the theme parks! Otherwise, parking is currently $14 a day; once you pay once though, you can visit the other parks on the same day and not have to pay for parking again!
Write back if you have any more questions!