If you have completed with this please tell me the detail as I am also going to update my server.
If you are planning to leave all laptops with OLD epo 4.6 and only planning to take rest of the machines to get managed from new EPO 5.3
You can perform the transfer machines as per Kb79283.
BUT< It depends on the products you are managing, If you have EEPC / MDE, version 7.1.2 or lesser version, this transfer machines option is not valid.
If you have MDE./EEPC 7.1.3, then you can open case with support, were there is a steps to transfer machines with MDE 7.1.3 from one to another EPO.
By chance, you don't have EEPC itself, and planning to perform this activity, you can proceed further.
Have a note of transferred machines will not automatically redirect to specific group and If you have any tags, need to assign manually.
Policies and tasks are to be re-configured.
Except the machine is moved to new EPO, rest all other activities will be manual process to get assigned those systems as applied.