SRM 8.2 supports vCenter and ESXi hosts that are 6.0 U3 and later versions. Now, following are some of the limitations:
1. Ensure hosts at recovery site are on a minimum 6.0 U3 --> VMware Product Interoperability Matrices
2. Since you are upgrading vCenter and hosts at production site to 6.5, ensure VM hardware version and tools are on a version that is supported by 6.0 hosts. If you upgrade them, you will have issues during recovery because hosts at the recovery site are still at 6.0.
3. If there issues during SRM test/recovery that is caused by a bug/known issue in 6.0 release, support will be limited/On best efforts because of the version
Hope that helps
Be aware that your remote site is running a version of vSphere which is no longer supported or updated.
Not sure I would want to run that for a DR site personally.
In addition to the previous comment which is important, I also recommend being very careful upgrading VM hardware, or deploying new VMs. Our standard recommendation is to upgrade the recovery site first, this is because when you upgrade the protected site, you could end up in a place where you have a VM that can run at the protected site (VM hardware supported on vSphere 6.5) but not at the recovery site (VM hardware supported on 6.5 can't run on 6.0 hosts). The VMs will still replicate, they just won't be able to be started at the recovery site until the hosts are upgraded.