Keep the car on ("ready" mode), it might pop up with a message saying car will turn off in an hour and you will need to click "keep on" or something like that. Turn off headlights, radio and air to keep more power. While it's in that mode it will keep 12V battery charged, and if the traction battery get too low it will start an engine as needed to recharge. A full battery charge might be enough for all day with such a small load. I had to do the same thing when camping to power my camper's propane heater and had maybe 10 miles of range and it lasted me around 6 hours before the engine started. More on reddit.com

Check the battery specifications for an Ampere-hour rating (abbreviated Ah). More on reddit.com

It depends entirely on that loads you want to run. The bigger question is why did the previous inverter fry? Fuses are a fail safe. If the current is too high they fail. Under normal circumstances they sit there doing nothing. More on reddit.com

Gather round kids for electrical 101. Watt = Volts x Amps So assuming you are using 12v nominal batteries, 5000W / 12V = 416A draw (assuming no power conversion losses. This would supply 5000W / 120v = 41.6 Amps at US standard wall outlet voltages. This is about what you can pull off a 2-3 standard US wall circuits before tripping a breaker, or about 6.75 hp for an internal combustion engine. 416A Amps is as much or more than large trucks use when starting, and a run of more than a few inches would require massive power cables (like 1 AWG wire for just a 4 foot wire run). More importantly, this is more than what most deep cycle batteries can safely provide for an extended time without severe issues like internal heat. A standard Group 31 deep cycle has roughly 110-130 Amp Hours of power at 12v, or 1300-1500 watt hours. 1500 watt hours / 5000 watt draw = 0.3 hours of power at full draw per deep cycle... in other words, you would completely drain a car-sized deep cycle battery in 20 minutes. 1000 milliamphours (mAH) = 1 AH, so your 10,000mAH lithium is really a 10AH battery... at 1/10th the capacity of a deep cycle, it would be drained in less than 2 minutes. Links to making your own battery back up using deep cycles batteries, a power inverter, and charge controller (roughly 1/3-1/4 the cost of a Jackery or other lithium set with similar capacity , and easier to expand or replace parts) : https://www.offgridweb.com/transportation/last-man-projects-200-diy-emergency-power-pack/ https://www.instructables.com/How-to-Build-a-Battery-Backup-Generator/ More on reddit.com