Rationalize the denominator of $ \frac{\sqrt{5}+\sqrt{2}}{\sqrt{5}-\sqrt{2}} $. The answer can be written as $ \frac{A+B\sqrt{C}}{D} $, where $ A $, $ B $, $ C $, and $ D $ are integers, $ D $ is positive, and $ C $ is not divisible by the square of any prime. If the greatest common divisor of $ A $, $ B $, and $ D $ is 1, find $ A+B+C+D $.