the width of the ellipse is 5 the radius is also 5.

area of ellipse = pi*a*b = pi*5*3

now we only have to deal with one half of the ellipse and larger circle.

so 0.5*pi*5*3

the area of the semicircle would be 0.5*pi*5^2

now area of semicircle minus area of half the ellipse and you get the area of the shaded region