Regular pentagon can be divided into 5 congruent triangles.
The area of a triangle =1/2*(base*height)
In our case base pf the triangle is the side of the pentagon, and the height of the triangle is an apotheme of the pentagon.
So, A(triangle)=(1/2)*10*5 =25 ft².
We have 5 triangles in pentagon,
so A(pentagon) =5*25=125 ft².