To solve this equation, we need to first combine all fractions on one side of the equation and simplify.

Given equation: 2y - 8/(y-5) + 10/(y^2-25) = y + 4/(y+5)

To simplify, we first need to factor the denominator in the second term on the left side:

y^2 - 25 = (y + 5)(y - 5)

Now substitute back into the equation:

2y - 8/(y-5) + 10/[(y + 5)(y - 5)] = y + 4/(y+5)

Find a common denominator for all terms:

2y(y+5)/(y+5)(y-5) - 8(y+5)/(y+5)(y-5) + 10/(y+5)(y-5) = y(y-5)/(y+5)(y-5) + 4(y-5)/(y+5)(y-5)

Simplify:

(2y^2 + 10y - 8y - 40 + 10) = (y^2 - 5y + 4y -20)

Combine like terms:

2y^2 + 2y - 30 = y^2 - y - 20

Rearrange into standard form:

2y^2 + 2y - 30 - y^2 + y + 20 = 0

y^2 + 3y - 10 = 0

Now factor or use the quadratic formula to solve for y.