To solve this equation, we can first simplify both sides by expanding the exponents:

(x-10)^7 = (x-10)^5

(x-10)(x-10)(x-10)(x-10)(x-10)(x-10)(x-10) = (x-10)(x-10)(x-10)(x-10)(x-10)

Next, we can cancel out the common factors on both sides:

(x-10)(x-10)(x-10)(x-10)(x-10) = (x-10)(x-10)(x-10)(x-10)

Now, we can divide both sides by (x-10)(x-10)(x-10)(x-10) to simplify further:

(x-10)(x-10) = (x-10)(x-10)

Finally, we can cancel out the common factors again:

x-10 = x-10

This equation is true for all values of x. Therefore, the solution to the equation is all real numbers.