Find the value of $\frac{5^{n+3}-6\times 5^{n+1}}{9\times 5^n-2^2\times 5^n}$

Factor out $5^n$ from both the numerator and the denominator:
$$\text{Numerator}=5^{n+3}-6\times 5^{n+1}=5^n\times 5^3-6\times 5^n\times 5^1=5^n(125-30)=5^n(95)$$
$$\text{Denominator}=9\times 5^n-2^2\times 5^n=5^n(9-4)=5^n(5)$$
Combine back into the fraction:
$$\frac{5^n(95)}{5^n(5)}=\frac{95}{5}=19$$