2x+ y- 5 isn't a line. Do you mean 2x+ y- 5= 0?

For the first line, y= -[(m-6)/(m-1)]x- 13/(m-1) (as long as m-1 is not 0). For the second line, y= -[(2m+1)/2m]x+ 3/m. At any point where they intersect y= -[(m-6)/(m-1)]x- 13/(m-1)= -[(2m+1)/2m]x+ 3/m. Solve that for x, in terms of m, of course, and use either of the two equaitions to determine y. Finally, put those values of x and y into 2x+ y- 5= 0 to get a single equation for m.