Question 29551
It might be helpful if you could draw yourself a diagram of the problem. I find that difficult to do on this site so I'll describe it in words.

You are going to compare two similar right triangles.

Right triangle 1 consists of the flagpole, which is the height of this triangle, and the base is the distance from the foot of the flagpole to the end of its shadow. This distance is 16 ft + 4 ft = 20 ft.

Right triangle 2 consists of the 5 ft-tall person, which is the height of this triangle, and the base is the distance from the persons feet to the end of his/her shadow, 4 ft. away.

Now in similar triangles, corresponding sides are proportional.
Let the height of the flagpole be h. We can write the following proportion based on the available information from the problem statement:

{{{h/20 = 5/4}}} In words:
 The height, h, of the flagpole is to the length of its shadow (20ft.) as the height of the person (5ft.) is to the length of his/her shadow (4ft.). Now we solve this proportion (equation) for h.

{{{h/20 = 5/4}}} Multiply both sides by 20.
{{{h = 20(5/4)}}}
{{{h = 25}}}ft.

The height of the flagpole is 25 ft.