Let the G.P. have first term $a$ and common ratio $r$.

Then $a_n = ar^{n-1}.$

Use the given condition: $\frac{a_3}{a_1} = 25.$

Now, $a_3 = ar^2, \quad a_1 = a.$

So, $\frac{a_3}{a_1} = \frac{ar^2}{a} = r^2 = 25.$

Hence, $r^2 = 25.$

We need to find: $\frac{a_9}{a_5}.$

Using $a_n = ar^{n-1}$, $a_9 = ar^8, \quad a_5 = ar^4.$

Therefore, $\frac{a_9}{a_5} = \frac{ar^8}{ar^4} = r^4.$

Since $r^2 = 25$, $r^4 = (r^2)^2 = 25^2 = 625 = 5^4.$

So, $\frac{a_9}{a_5} = 625 = 5^4.$

Checking options:

• A: $5^3 = 125$
• B: $2(5^2) = 50$
• C: $4(5^2) = 100$
• D: $5^4 = 625$

Therefore, the correct option is D.