Bought a brand new battery. Tested at only 5.79v

It's possible that the new battery is simply defective - like anything it's possible to buy a duff one. That said it could also just need a decent charge and I'm not sure a 20 min drive is going to be enough, the fact that it went up at all is a good indicator that the battery is ast least taking a charge. If you have a proper battery charger at home I'd suggest giving it a full charge and seeing if it holds it properly, if it doesn't charge fully or won't hold it then it's time to go back to Walmart and ask for a replacement.

Based on what you've posted, you have a battery from WalMart that shouldn't have gone into this car. You should remove the new battery, exchange it for another. Before you put it in the car, have it charged and professionally tested. You are doing this extra stuff because you most likely have other problems because it stalled in the driveway. You need a good fully charged battery to diagnose other problems. After the new charge and tested battery is installed the charging system needs checked. You should have both battery cables cleaned at both ends. You should see 13.8 to 14.5 volts at battery terminals with engine running.