The desert has 3/5 fewer palm trees than the forest, and since the forest has 5000 palm trees, the desert has 3/5*5000 = <<3/5*5000=3000>>3000 fewer palm trees.
The total number of palm trees in the desert is 5000-3000 = <<5000-3000=2000>>2000
Together, the desert and the forest have a total of 5000+2000 = <<5000+2000=7000>>7000 palm trees.
#### 7000