I don't think there is any reason not to trust most online calorie-expenditure calculators, I mean, suspecting they are erroneous is baseless unless you have your own bomb calorimeter. They are probably as close of an estimate as anyone could come up with.

FYI, just throwing some numbers in to one of these: TDEE Calculator , it looks as if you have a BMR of about 1600 kCal, if you really do exercise 2-3 hours or so a day, that could be well north of 1000 kCal burnt, assuming some hard effort. given a rough TDEE of 2600, tack on 400 for a growing young man , and 3000 kCal should be about what you need a day. I suspect that 5000 kCal/day would be putting some weight on you if it were being consumed consistantly.