5^9*5^3:5^10

To simplify the expression \( \frac{5^9 \cdot 5^3}{5^{10}} \), you can use the properties of exponents.

First, use the property that states \( a^m \cdot a^n = a^{m+n} \):

\[ 5^9 \cdot 5^3 = 5^{9+3} = 5^{12} \]

Next, substitute this back into the expression:

\[ \frac{5^{12}}{5^{10}} \]

Now use the property that states \( \frac{a^m}{a^n} = a^{m-n} \):

\[ \frac{5^{12}}{5^{10}} = 5^{12-10} = 5^2 \]

Finally, calculate \( 5^2 \):

\[ 5^2 = 25 \]

Therefore, the final result is:

\[ \boxed{25} \]