Should I close my inactive credit card account?

First, the background: I currently have three store cards (two are inactive), a credit/debit card through my bank (doesn't appear on my credit report), a Mastercard, a USAA Amex card, and I have been an authorized user on a card of my parents' for like ten years. My credit score was 792 last year when I... show more First, the background:
I currently have three store cards (two are inactive), a credit/debit card through my bank (doesn't appear on my credit report), a Mastercard, a USAA Amex card, and I have been an authorized user on a card of my parents' for like ten years. My credit score was 792 last year when I was approved for a loan for my condo (no late payments). I also have a student loan as well that I have been paying for six years (no late payments). I use my Mastercard and Amex card every month and pay both in full. I use my one active store card maybe eight months of the year and always pay it in full.

I have been considering closing one of my store accounts (not associated with Visa or MC, just a store card) b/c it is for a store I only go to when I am visiting family. I have heard that closing accounts will count against me, but I am not so sure about this one since it is already inactive. Should I close it or leave it open? I haven't used it in four years.
Update: My oldest card is 10 years old, though I have been an authorized user on another card for 15 years. My other active cards are 7 years old and 6 months old. The inactive card I am considering closing is 6 years old. The monthly payment is listed as $0 on my credit report and it says N/A under Credit Limit. I... show more My oldest card is 10 years old, though I have been an authorized user on another card for 15 years. My other active cards are 7 years old and 6 months old. The inactive card I am considering closing is 6 years old. The monthly payment is listed as $0 on my credit report and it says N/A under Credit Limit. I assume because the status of the card is inactive.
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