How many ways can 10 letters be posted in 5 post boxes, if each of the post boxes can take more than 10 letters?

Question

I have this question:

How many ways can 10 letters be posted in 5 post boxes, if each of the post boxes can take more than 10 letters?

I solved using the approach that: 10 letter can be put in each letter box hence total ways = $10*10*10*10*10=10^5$

But the actual answer is 5 to the power 10, how is this possible?

Answer 1

Each of the 10 letters can be stored in any of the 5 postboxes. So, the first letter has 5 options(postboxes),so does the second letter and so on and so forth for all of the 10 letters. i.e. $5*5*5*….*5$ (upto 10 times) = $5 ^ {10}$.