Let,

x1=x2=s

x3=x4=t

x5=r

Any element in this subspace is,

[x1 x2 x3 x4 x5] = [s s t t xr]

Write as,

[s s 0 0 0] + [0 0 t t 0] + [0 0 0 0 r]

Factor,

s[1 1 0 0 0] + t[0 0 1 1 0] + r[0 0 0 0 1]

We can see that,

{[1 1 0 0 0], [0 0 1 1 0], [0 0 0 0 1]}

Is the basis for this subspace.