Welcome to VMTN. :-)
Below are few major pointers that I would take care before upgrading.
1. Since you would be updating the major version from 5 to 6, follow the VMware Update sequence. It details which component needs to be updated first during the update process.
2. Make sure hardware supports intended ESXi version. In you case, it does but there's no scope of future upgrade to 6.5.
3. Make sure connected solutions in your environment support ESXi 6U3. For example, take storage solution. Make sure it would support ESXi 6.0U3 else you may face performance issues.
4. Make sure your follow the NIC and storage controller firmware and driver version match as per VMware HCL.
Let us know if you have any query.