What is the minimum value of (sin²A + 5 sin A + 1)/sin A for 0 < A ≤ π/2?

Let t = sin A where 0 < t ≤ 1. Expression = t + 5 + 1/t. Function f(t) = t + 1/t + 5 is decreasing on (0,1], so minimum on this interval is at t = 1, giving 1 + 1 + 5 = 7.