Take four of the five points at the bottom as the base of the pyramid. There are four of the five bases and the height is one of the five points at the top and bottom, so there are 5 ***5 = 25 quadrilaterals with four points at the bottom.

There are also 25 quadrangular pyramids, and the other one has a bottom.

A quadrangular pyramid with any two sides of a regular pentagonal prism as the bottom and any one of the other six points as the vertex has 6 vertices, and the bottom is 2=5*4/2= 10, so there are 6 * * * 10 quadrangular pyramids in total.

A quadrangular pyramid consisting of two parallel sides on two bottom surfaces, where any two points on the upper bottom surface are parallel to the straight line formed by two points on the lower bottom surface, the combination of two out of five is 5*4/2= 10, and the other six points form a quadrangular pyramid of 10*6=60.

To sum up, the quadrangular pyramid has 25+25+60+60= 170.