To simplify the given expression, we need to combine all terms into a single trigonometric function.

Let's start by converting the trigonometric functions to their respective identities.

5/cosx - 2/sinx = 10/sin2x

Firstly, we need to express sin2x in terms of sinx and cosx.

sin2x = 2sinxcosx

Substitute back into the equation:

5/cosx - 2/sinx = 10/(2sinxcosx)

Now, combine the terms on the right side:

5/cosx - 2/sinx = 5/(sinx * cosx)

Now, we need to find the least common denominator, which is sinx * cosx:

(5sinx - 2cosx)/(sinx cosx) = 5/(sinx cosx)

Now, cross multiply:

5sinx - 2cosx = 5

Rearrange the equation to isolate one of the variables:

5sinx = 5 + 2cosx

Divide by 5:

sinx = (5 + 2cosx) / 5

Therefore, the simplified form of the given expression is sinx = (5 + 2cosx) / 5.