I think I understood your problem, the key here is that you are given a similar triangle, the 6ft person when he is 5 ft from the tip of the shadow.. that's your 2nd triangle.

Use that one to get either the angle for the triangle (which will be the same angle for the triangle formed by the streetlight and the long shadow), or simply use the similar triangles rule and solve for the height of the streetlight.

Let me know if I interpreted your problem correctly.