diff --git a/lib/morpheus.gi b/lib/morpheus.gi
index d0a8e7c7344..4b0d8f5a152 100644
--- a/lib/morpheus.gi
+++ b/lib/morpheus.gi
@@ -535,6 +535,12 @@ local hom, gens, c, ran, r, cen, img, u, orbs,
   while Size(u)<Size(g) do
     if Size(u)>1 then SortBy(c,Size);fi; # once an outside class is known, sort
     of:=First(c,x->not Representative(x) in u);
+
+    if of=fail then
+      # rarely reps are in u
+      of:=First(c,
+        x->ForAny(GeneratorsOfGroup(g),y->not Representative(x)^y in u));
+    fi;
     if MemoryUsage(Representative(of))*Size(of)
       # if a single class only requires
       <10000
diff --git a/tst/testbugfix/2024-05-06-Isom.tst b/tst/testbugfix/2024-05-06-Isom.tst
new file mode 100644
index 00000000000..80ebd3151fb
--- /dev/null
+++ b/tst/testbugfix/2024-05-06-Isom.tst
@@ -0,0 +1,7 @@
+# Fix #5708
+gap> G:=Group([ (2,11,20)(3,10,19)(4,9,12)(5,8,13)(6,15,17)(7,14,18),
+> (2,20)(3,4)(5,7)(8,18)(9,19)(10,12)(13,14)(15,17),
+> (1,2)(3,20)(6,18)(7,19)(8,12)(9,11)(13,15)(16,17) ]);;
+gap> H:=Group([ (1,2,3,4,5), (3,4,5), (6,7) ]);;
+gap> IsomorphismGroups(G,H)<>fail;
+true