How to Find p-adic Expansions Part 2

Part 1 deals with positive integers.
Part 2 extends to all integers.
Part 3 deals with special fractions.

[potatootter]

Hello, I do not understand the following parts:
1) How did you obtain 1*5^0?
You mentioned along the lines of 4+1=5, 5*5^0=5^1, therefore it cancels out? But cancelled out what?

2) How did you obtain 1*5^1 (in red)?

3) How did you obtain 4*5^2?
Where did the 4 comes from? Why not 2 or 3?

So on and so forth.
Thanks.