Forming a number of 3 powers of 5

If you consider numbers in base 5.

You can write $781_{10} = 11111_5 = 5^4 +5^3+5^2+5^1+5^0 = 625 + 125 + 25 + 5 +1$

There are only $^5C_3 = 10$ ways to express a number as a sum of 3 different powers of 5.

5^x + 5^y + 5^z <= 781 (x,y,z distinct)

max is 5^4, now lets check the limit i.e 5^4 + 5^3 + 5^2 <=781

so the powers can vary from 0 to 4

so the answer is 5 choose 3 = 10