we know that
Euler's formula states that Number of Faces plus the Number of Vertices (corner points) minus the Number of Edges is always equals 2
F+V-E=2
in this problem
F=7
V=2*5+5*4---> 30-----> (two pentagons and five rectangles)
E=?
E=F+V-2
E=7+30-2
E=35
the answer is
the number of edges is 35