β属于（π/2,π）,cosβ=-5/13,sinβ＞0,∴sinβ=12/13
sin(α+β)=-3/5=sinαcosβ+cosαsinβ=-5/13·sinα+12/13cosα=-3/5 ①
又（0,π/2）,β属于（π/2,π）,所以π/2＜α+β＜3/2π,
又sin(α+β)=-3/5＜0,所以π＜α+β＜3/2π,∴cos(α+β)＜0,∴cos(α+β)=-4/5
cos(α+β)=cosαcosβ-sinαsinβ=-5/13cosα-12/13sinα=-4/5 ②
联立①②,-5/13·sinα+12/13cosα=-3/5、-5/13cosα-12/13sinα=-4/5
求解得sinα=63/65