You can use a separate power plug, but for ease of switching between trailers and tow vehicles, and for availability of parts, it makes sense to use standard connectors. The 7-way connector (6 flat blades around a round centre pin) known as the "RV" or "Bargman" type is essentially the standard, and includes pins to connect the battery power, as well as electric brakes
(just don't use the ones you don't need).
The flat 5-pin (presumably the one with 5 round pins in a row) connector is not really very common now. The two-pin version of the same thing is readily available, but those connectors don't have very large contacts or wires, so they're not good for much current - better suited to lights
than battery power supply.
There are quite a few discussions here in the forum of battery connection details, once you've picked a connector; I suggest a search for "isolator" or "solenoid" to find the appropriate topics. Also, there are some diagrams and other information the Resources section (menu on the left side of the page).