The cross-product works this way

  (-1,3,5) x (0,a,1) = det 


In the right side i, j, and k are the unit vectors along x-, y- and z-coordinate axis.


Let's consider x-component of the cross-product. 
According to the rules of calculating this determinant, we should cross it out the first line and first row 
in this matrix and calculate the determinant of the remaining 2x2-matrix

    det  = 3*1 - 5*a = 3 - 5a.


It should be equal x-coordinate of the vector (-2,1,-1), which is -2.


It gives us this equation

    3 - 5a = -2.


It is easy to solve

    3 + 2 = 5a

      5   = 5a

      a   = 5/5 = 1.


ANSWER.  a = 1.