ScalCG6

I recently put a new alternator in my car cause I noticed my lights starting to dim out while driving. So I change alternator and car start right up , maybe 5-10 minutes later car just shuts off and I’m completely confused I checked for spark it was good checked the fuel pump all good , so I’m wondering is it a faulty alternator or do I need a new battery cause my battery is kind of old but I got it recharged recently and it was working fine prior PLEASE HELP !!!!!!