I'm not sure if this scenario is supported but before thinking of the support side ,
I'f your Customer will upgrade the VM Hardware version of the VMs in the production side he will no longer can use those VMs on ESXi 5.5.
And he needs to bare in mind theVMFS 6 that cannot be run on ESXi 5.5
What type of DR recovery product is in use like (vSphere SRM) and what is the replication method is being used in your customer environment (is it vSphere replication or 3rd party replication) ?
Customer using Dell Protection suite as a recovery solution (RP4VM). They are not using SRM/vSPhere replication.
It is always advisable to have a similar software version to be used at Protected Site & DR Site ,though you are using any DR Solution.
Please check the VMWARE HCL Guide to check compatibility.
In my scenario, customer has IBM X3850 X5 at production site which will support up to vsphere 5.5 U3 but they wish to upgrade it to vSphere 6.5 , they wanted to replace the production server procuring new hardware, however they wanted to keep the same server at DR Site . They don't have budget to replace both the servers. Do I have any options at the moment. ???