It has hamiltonian circuit
By Dirac's Theorem
deg(u) $\geq \left \lfloor \frac{n}{2} \right \rfloor$
here $\left \lfloor \frac{n}{2} \right \rfloor = \left \lfloor \frac{5}{2} \right \rfloor=2$
deg(A)= 2
deg(B)=3
deg(C)=3
deg(D)=4
deg(E)=2
By definition: A closed walk which traverse all the vertices of graph exactly onces( except starting and ending) has hamiltonian circuit.
ADECBA is the desired circuit