To simplify this expression, we can first use the sum-to-product identities for sine:

sin(a) + sin(b) = 2sin((a+b)/2)cos((a-b)/2)

Applying this formula to sin(5x) + sin(3x):

sin(5x) + sin(3x) = 2sin((5x+3x)/2)cos((5x-3x)/2)
= 2sin(4x)cos(x)

Next, for the denominator cos(6x)sin(10x) - cos(10x)sin(6x), we can use the product-to-sum identities for cosine:

cos(a)sin(b) - cos(b)sin(a) = sin(b-a)

Applying this formula to cos(6x)sin(10x) - cos(10x)sin(6x):

cos(6x)sin(10x) - cos(10x)sin(6x) = sin(10x-6x)
= sin(4x)

So the original expression becomes:

(2sin(4x)cos(x)) / sin(4x)

= 2*cos(x)