we know that
sec θ=1/cosθ
if θ is in Quadrant IV--------------> sec θ is positive, because the cosθ is positive
sinθ=-1/5
sin²θ+cos²θ=1--------------> cos²θ=1-sin²θ-----------> 1-(1/5)²=24/5
cosθ=√(24/5)----> 2√6/√5
secθ=1/cosθ--------> 1/(2√6/√5)---------> √5/(2√6)=√30/12
the answer is secθ=√30/12