Ideally in this case, they recommend to upgrade in this scheme:
Production:
> vCenter from 5.5 U3 TO 6.0 u3
> SRM from 5.8.1 to 6.1.2
> vCenter from 6.0 U3 to 6.5 U1
> SRM from 6.1.2 to 6.5.1
And then the same on the recovery site.
If you jump vCenter to 6.5 directly, there might be issues while upgrade SRM from 5.8.1 to 6.1.2
# Suhas