SetLogFile("a5.log"); 

G := AlternatingGroup(5);
AG := SymmetricGroup(5);
AK := Classes(AG);
K := Classes(G);
AK;
K;
K2 := Class(G,K[2][3]);
K3 := Class(G,K[3][3]);
X235 := {<a,b,(a*b)^(-1)> : a in K2, b in K3 | Order((a*b)^(-1)) eq 5};
#X235;
th := AG!(1,2);
th;
{x: x in X235| <th*x[1]*th*x[1],th*x[2]*th*x[2]> eq <Id(AG), Id(AG)>};
th := AG!(1,2)(3,4);
th;
{x: x in X235| <th*x[1]*th*x[1],th*x[2]*th*x[2]> eq <Id(AG), Id(AG)>};

UnsetLogFile();