To solve for Y(s), you would divide by the factor (s²+s+5/4):
Y(s) = ( 1/s-e^(-pi*s)/s+s )/(s²+s+5/4).
I'm assuming there is more to this problem. Your equation looks like the Laplace transform of a differential equation. Are you supposed to find the inverse transform, f(t) ? If so, you would complete the square in the denominator,
s²+s+5/4 = (s+1/2)² + 1,
then split the fraction into three terms, then use standard tables to find the inverse transform.