In the figure below, $ABDC,$ $EFHG,$ and $ASHY$ are all squares; $AB=1$, $EF=1$, and $AY=5$.
What is the area of quadrilateral $DYES$?
[asy]
size(5cm);
defaultpen(black+1);
pair a=(0,5); pair b=(1,5); pair c=(0,4); pair d=(1,4); pair e=(4,1); pair f=(5,1); pair g=(4,0); pair h=(5,0); pair y=(0,0); pair s=(5,5);
draw(a--s--h--y--a);
draw(c--d--b, gray);
draw(g--e--f, gray);
draw(d--y--e--s--d);
dot(a); dot(b); dot(c); dot(d); dot(e); dot(f); dot(g); dot(h); dot(y); dot(s);
label("$A$",a, NW);
label("$B$",b, N);
label("$C$",c, W);
label("$D$",d, SE);
label("$E$",e, NW);
label("$F$",f, E);
label("$G$",g, S);
label("$H$",h, SE);
label("$Y$",y, SW);
label("$S$",s, NE);
[/asy]
15
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