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I hope you mean 6 quarts, not 6 gallons. And yes, you need to get the oil changed again if you want the car to last.
Yes, change the oil. Every 5,000 miles is tolerable but I personally do every 3,000
5,000 is standard for most cars vehicles produced in the last 20 years, 3k is what I do on my 92 pickup and 96 Civic.