Let's draw a line such that it goes through $E$ and
perpendicular to $AB$ and $CD$.It intersects $AB$
at $F$ and $CD$ at $G$.We also can say that $BF = CG , AF = DG$.
We can form four equations:
$DE^2 = EG^2 + DG^2...(i)$
$CE^2 = EG^2 + CG^2...(ii)$
$AE^2 = EF^2 + AF^2...(iii)$
$BE^2 = EF^2 + BF^2...(iv)$
$(iv) -(iii) \Rightarrow BE^2 - AE^2 = BF^2 - AF^2 \Rightarrow 20 = BF^2 - AF^2$
$ = CG^2 - DG^2$
$(i) - (ii) \Rightarrow DE^2 = DG^2 - CG^2 + CE^2 = -20 + 25 = 5$
$\therefore DE = \sqrt{5}$