To simplify the expression \(\frac{5^{653}}{5^{651}}\) using the quotient rule of exponents, we use the rule that states:
\[ \frac{a^m}{a^n} = a^{m-n} \]
In this case, we have:
\[ \frac{5^{653}}{5^{651}} = 5^{653-651} = 5^{2} \]
So, the expression simplifies to \(5^2\), which is not listed among the options provided.
If we consider the original prompt that presents only a number (5653), and assume you're asking to find the simplification of \(5^{653} / 5^{651}\), then:
\[ 5^2 = 25 \]
None of the choices exactly represent \(5^2\) or 25, but considering the options:
- 51 (5 to the 1th power is incorrect as it's just 5)
- 518 (5 to the 18th power is incorrect)
- 53 (5 cubed is incorrect)
- 59 (it is not correct)
The closest representation for \(5^{653}/5^{651}\) is \(5^2\), which equals \(25\), but it's not provided in the options. If considering the exponent itself and not the base, we would use that logic to clarify the simplification output.
For clarity, the correct answer is that the simplification of \(5^{653}/5^{651} = 5^{2}\).