first you choose 5 boxes parmi 10 boxes :you have C(10,5)=10!/((5!)*(10-5)!)  possibilities and then you place your vowels in alphabetical order in your 5 boxes:you have one possibility. So you have C(10,5)*1 possibilities.

After that,for one of your C(10,5) possibilities,you complete the other boxes with the 5 other letters in order without repetitions :you have 5! possibilities.

So,totaly,you have C(10,5)*5! special arrangements possible cad: 30240 special arrangements of GELATINOUS.