Did the engineer tell you the reason why he recommended v6.0?
The only reason against v6.5 that I can think of, would be a hardware incompatibility.
If your host support ESXi 6.5, I'd say go for it.
I agree with André.
As long as the hardware is compatible there is no reason why you should not update to 6.5
You could check for yourself if your hardware is compatible using the VMware Matrix:
Also check if any upgrade path incompatibility exists:
As mentioned already there is nothing bad with 6.5. I believe the engineer mentioned this because of your hardware, maybe some of your components might not have custom drivers. This was my case and had to stay on 6.0 till I upgrade my hardware. What I can say is ask the support engineer one more time to really specify why he mentioned that you can't do the upgrade.