∵2sina+cosa=0
∴ cosa=-2sina
∴ sin2α-3sinαcosα-5cos2α
=(sin²a-3sinacosa-5cos²a)/(sin²a+cos²a)
=(sin²a+6sin²a-20sin²a)/(sin²a+4sin²a)
= -13sin²a/(5sin²a)
=-13/5