ESXi

I am using an ESXi 6.0 and want to upgrade to ESXi 6.5. Can I switch directly or do I need to upgrade in sequence? ESXi 6.0 has some patches, can I first install them and then upgrade to ESXi 6.5?

If you are using ESXi 6.0, you can upgrade directly to ESXi 6.5. There is no order for this.
But you should remember that. Before upgrading, you must check the hardware compatibility of the physical server. If your physical server supports ESXi 6.5, you must update firmware before upgrading. It is very important that you keep the firmware versions up to date.

VMware Compatibility Guide - System Search

What is the physical server brand model? Let's check for hardware compatibility.

you can upgrade it to the ESXi 6.7 by ESXCLI or VUM without need to install these patches (and also easily downgrade it  if there is a problem anyway) So if you need a special patch in ESXi 6.0, instead of that download and install same time published patch for ESXi version 6.5