You can choose the points from the given points as follows:
2 from Line 1(L1) and 1 from Line 2(L2) = (5C2) * (5C1) = 10*5 = 50
2 from L2 and 1 from L1 = (5C2) * (5C1) = 10*5 = 50
2 from L1 and the non collinear point = (5C2) * (1C1) = 10
2 from L2 and the non collinear point = (5C2) * (1C1) = 10
1 from L1, 1 from L2 and the non collinear point = (5C1) * (5C1) * (1C1) = 25
Answer= 50+50+10+10+25 = 145 Triangles