Let's simplify the expression step by step:

ctg(3π/2 - a) = 1/tan(3π/2 - a) = 1/(-tan(a)) = -cot(a)

sin(a - 5π/2) = sin(a + π/2) = cos(a)

tan(π/2 + a) = -cot(a)

cos(7π/2 + a) = cos(3π/2 + 2π + a) = cos(3π/2 + a) = -sin(a)

Now, plugging these results back into the original expression:

cot(a) - cos(a) + (-cot(a)) (-sin(a))
= -cot(a) - cos(a) + cot(a) sin(a)
= -cos(a)

Therefore, the simplified expression is -cos(a).