tl;dr: skip to the last paragraph for what you need to know to fix your problem.
The groove on E3D hot ends does not match the groove on most other groove-mount hot ends. This does cause issues. There was a good reason for the metal E3D not matching other (PEEK and PTFE) hot ends, but that reason is somewhat irrelevant since the most common mounting style has changed. It used to be that groove-mount hot ends (and hot ends without a groove mount - just a plain cylinder) were mounted using two screws that would grip the hot end tightly on either side. You can see the two holes that the screws would run though the extruder at the hot end mounting hole in
this image. For this to work properly, the screws had to bite into the hot end material, which was usually PEEK or PTFE. If you now replace that material with aluminum (á la E3D), the groove has to be wider because the screws are unable to bite into the aluminum as easily as they could in PEEK or PTFE. The reason this is irrelevant now, is that everyone uses a groove mount plate or similar instead of screws for mounting the hot end. It would probably have been a better choice for E3D to have maintained the standard groove mount width, since screw mounts like that are so rare now anyways. But, it's now too late for them to make that change without upsetting the significant number of people that have designed extruders and printers around their now-popular hot end.
I'm sure you didn't want that whole history lesson, but I like to educate people on the reasons behind the different design choices that go into RepRap hardware and electronics.
Your solution:
The best you could probably do right now is to create some shims to thicken the aluminum plate, adding (5.65mm - 4mm =) 1.65mm. The easiest thing would be to take some tape, layer it on top (or bottom) of the aluminum plate around the slot until it is a little over 1.65mm thick (so that the hot end fits tightly), and trim the tape to match the slot in the aluminum plate. Push the hot end in place, ensuring that it fits tightly with out room to move. Then later you could print a shim to replace the tape, which would look more professional and last longer than the makeshift tape shim.