Here is the list of (5-1)! = 24 circuits.
A-B-C-D-E-A <=> 500 + 305 + 320 + 302 + 205 = 1632 <=> A-E-D-C-B-AA-B-C-E-D-A <=> 500 + 305 + 165 + 302 + 185 = 1457 <=> A-D-E-C-B-A
A-B-D-C-E-A <=> 500 + 360 + 320 + 165 + 205 = 1550 <=> A-E-C-D-B-A
A-B-D-E-C-A <=> 500 + 360 + 302 + 165 + 200 = 1527 <=> A-C-E-D-B-A
A-B-E-C-D-A <=> 500 + 340 + 165 + 320 + 185 = 1510 <=> A-D-C-E-B-A
A-B-E-D-C-A <=> 500 + 340 + 302 + 320 + 200 = 1622 <=> A-C-D-E-B-A
A-C-B-D-E-A <=> 200 + 305 + 360 + 302 + 205 = 1372 <=> A-E-D-B-C-A
A-C-B-E-D-A <=> 200 + 305 + 340 + 302 + 185 = 1332 <=> A-D-E-B-C-A
A-C-D-B-E-A <=> 200 + 320 + 360 + 340 + 205 = 1425 <=> A-E-B-D-C-A
A-C-E-B-D-A <=> 200 + 165 + 340 + 360 + 185 = 1250 <=> A-D-B-E-C-A
A-D-B-C-E-A <=> 185 + 360 + 305 + 165 + 205 = 1220 <=> A-E-C-B-D-A
A-D-C-B-E-A <=> 185 + 320 + 305 + 340 + 205 = 1355 <=> A-E-B-C-D-A
The Optimal Solution is shown below.