There is almost always better technology available than the technology that we actually buy and use. COST is usually the limiting factor, not technological capability.
5000W 12V input inverters - not impossible - not even hard. That's 427 amps at 12V. If the run is short (a couple feet) 4/0 cables should work (and are common and inexpensive at welding supply houses), and a bank of batteries with a total AH rating needed to supply that many amps for however long it is you want it to run, and rated discharge rates appropriate for the current divided by the number of batteries. The harder part would be charging such a bank back up again quickly.
Usually such setups are used for off-grid solar installations, where the average watts used is much lower, but can occasionally spike for running a well pump or some other short-duration high-current load.