Eulerian and Hamiltonian Graphs · Challenge problem

Five landmasses $A,B,C,D,E$ are joined by bridges $AB, AC, AD, BC, BE, CD, CE, DE$ (eight bridges, no others). City engineers may close (permanently remove) some bridges to simplify upkeep, but still want SOME walk that crosses every remaining bridge exactly once (not necessarily a closed loop). What is the minimum number of bridges that must be closed?