To simplify the given expression:

Factor the denominators in both terms of the numerator and in the denominator:

(y+5)/(y^2-7y+10) = (y+5)/((y-2)(y-5))(y-2)/(y^2-3y-10) = (y-2)/((y-5)(y+2))

Therefore, the numerator becomes ((y+5)/((y-2)(y-5)) - (y-2)/((y-5)(y+2)))

(11y+6)/(y^2-4) can be factored as (11y+6)/((y-2)(y+2))

Combine the two terms in the numerator using a common denominator:
((y+5)(y+2) - (y-2)(y-5))/((y-2)(y-5)(y+2))

This simplifies to ((y^2 + 7y + 10) - (y^2 - 7y + 10))/((y-2)(y-5)(y+2))
= (2*7y)/((y-2)(y-5)(y+2))
= (14y)/((y-2)(y-5)(y+2))

Get the final result by dividing the numerator by the denominator:
(14y)/((y-2)(y-5)(y+2)) ÷ ((11y+6)/((y-2)(y+2)))

Multiplying by the reciprocal of the denominator gives:
(14y)/((y-2)(y-5)(y+2)) * (((y-2)(y+2))/(11y+6))
= 14y(y-2)(y+2)/((y-2)(y-5)(y+2)(11y+6))
= 14y/((y-5)(11y+6))

Therefore, the simplified expression is 14y/((y-5)(11y+6))