Drawing shows that the intersection points of the straight line y=2x-3 and the coordinate axis are (0, -3) and (3/2, 0) respectively. Note: Make x y zero respectively.

And because the linear functions y=kx+5 and y=2x-3 intersect at the same point a on the axis, then k must be negative, and point b is (0,5), that is, y=kx+5 must pass through this point.

According to the above conditions, point A is the same point of two straight lines, so the formula of function y=kx+5 can be obtained.

Then a (3/2,0) b (0,5), c (0 0,3)

Take bc as the base, A as the height and bc as the length of 8.

So the area of the triangle is 8*3/2* 1/2=6.