The formula to find the area of a triangle is:
[tex]A=\frac{1}{2}b\cdot h[/tex]As you know the area and height, solve the equation for b:
[tex]\begin{gathered} \frac{A}{h}=\frac{1}{2}b \\ \\ \frac{2A}{h}=b \end{gathered}[/tex]Then, the base of the give triangle is: 7 ft[tex]\begin{gathered} b=\frac{2(17.5ft^2)}{5ft} \\ \\ b=\frac{35}{5}ft \\ \\ b=7ft \end{gathered}[/tex]