Ideally in this case, they recommend to upgrade in this scheme:
> 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
direct upgrade of SRM 5.8.1 to 6.5 is Not Supported. You can check this in the KB: VMware Knowledge Base
The products SRM and VC are in a lock-step for these versions or if you want to upgrade SRM to a certain version you have to check that the VC version is supported for this SRM. This is not valid for the latest SRM 8.1, that is compatible with vSphere 6.0. Update 3, vSphere 6.5, vSphere 6.5 Update 1, vSphere 6.7.
Hope that this help,