Final answer:
To prove the divisibility of the given number by 7, we can simplify the expression and show that the resulting number is divisible by 7.
Step-by-step explanation:
We need to prove the divisibility of the number 5^5 - 5^4 + 5^3 by 7.
To do this, we can simplify the expression first.
5^5 - 5^4 + 5^3 = 5^3(5^2 - 5 + 1).
Now, let's focus on the expression inside the parentheses.
5^2 - 5 + 1 = 25 - 5 + 1 = 21.
So, the expression becomes 5^3(21).
To prove divisibility by 7, we need to show that 21 is divisible by 7.
21 ÷ 7 = 3, which means 21 is divisible by 7.
Therefore, since 21 is divisible by 7, the number 5^5 - 5^4 + 5^3 is also divisible by 7.