For how many integers from 1 through 99,999 is the sum of their digits equal to 10? I am doing some practice in counting, and came to this question:

For how many integers from $1$ through $99999$ is the sum of
their digits equal to $10?$

I am unsure, how to handle this question - anyone that got a idea of, how to do this kind of questions?
Count the number of ways of assigning values (any values) to non-negative integers $x,y,z,u,v$ that add up to $10$, using the algorithm in this answer of mine (with $14$ instead of $20$, and four instead of three). Then subtract $5$ to discard the extraneous solutions $(x,y,z,u,v) = (10,0,0,0,0),(0,10,0,0,0)$ etc.
Hint: There are $5$ digits - So, $a+b+c+d+e = 10$ That is .. there are $5$ boxes and $10$ balls to be put in them. The only condition is that all the balls cannot go into the same box.