$2^{25}+2^{27}$ is divisible by:

The correct option is 10.

To find which of the given options divides the expression $2^{25}+2^{27}$, we can simplify the expression by factoring out the greatest common power of 2.

First, let us write the expression:
$2^{25}+2^{27}$

We can express $2^{27}$ as $2^{25}\times 2^2$. Substituting this back into the expression gives:
$2^{25}+2^{25}\times 2^2$

Now, factor out the common term $2^{25}$:
$2^{25}\times (1+2^2)$

Next, simplify the terms inside the parentheses. Since $2^2=4$, we have:
$1+4=5$

Substituting this value back, the expression becomes:
$2^{25}\times 5$

We can rewrite $2^{25}$ as $2^{24}\times 2$ to explicitly show a factor of 10:
$2^{24}\times 2\times 5$

Since $2\times 5=10$, the expression simplifies to:
$2^{24}\times 10$

Because the simplified expression contains 10 as a factor, the entire number is completely divisible by 10.