5 Cans Together...

Image of the constructions i did here

I divided the shape up into 3 different shapes. First was a square, drawn by connecting the midpoints of the outer 4 circles. Then i drew lines from the center of each of the outer circles to where they are tangent with the perimeter.

Using special right triangles, one knows each side of the square is $2.5 \sqrt{2}$ , and the area of it would be $(2.5{\sqrt{2}})^2$ .

Then we find the area of each of the identical outer rectangles, which have a length equal to that of the square , $2.5\sqrt{2}$ , and a height equivalent to the radius, 1.25. The total area of the 4 rectangles would be $4 (2.5{\sqrt{2}} * 1.25)$ or $12.5\sqrt{2}$ .

Finally, we have 4 quarter circles remaining, and their areas combines to make $1.25^2{\pi}$ .

We add the 3 areas together, and subtract the 5 circles to get our final answer:

$(2.5{\sqrt{2}})^2+12.5\sqrt{2}+1.25^2{\pi})-5(1.25^2{\pi})=\boxed{~10.543}$

$(\sqrt{12.5}+2.5)^2-5*\pi*1.25^2-4*(1.25^2-0.25*\pi*1.25^2)=\boxed{10.543}$