No need to know what else may be plugged into the circuit, as there is much else to consider first:
a) Given a 4.9A steady-state current draw at 115 VAC, that comes to 563 wat ts. Less than a standard hair-dryer (~1,200 watts). No big deal, even for a 15A conventional circuit (1,725 watts). Even one that shares a few other small things. b) Given that the typical surge for a conventional AC unit is very roughly eight (8) times the steady-state, the circuit must be able to withstand a v ery roughly 38 amp surge. This is well within the capacities of a standard
15A or 20A circuit breaker - AS LONG AS THERE ARE NO OTHER LOADS.
*And as l ong as the breaker is functioning properly*. c) Most recent (modern) window units come with a GFI device mounted on the plug. So there should be no intrinsic danger of fire or overheating. d) Never, ever use an extension cord with a window AC unit. Ever.
With these in mind:
Plug them in, and let them rip. Should a circuit breaker blow, you will kno w what is shared. Remove those shared items and start over. If both units h appen to be on the same circuit, use only one (1) at a time.
Ideally any AC line should be (at least) a dedicated 20A circuit using (at least) 12-gauge wire. Then there would be no discussion. If this is a renta l, I feel her pain. If this is owned, install the dedicated circuits as-nee ded. They will not go to waste.
Peter Wieck Melrose Park, PA