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Closing cards doesn't have an immediate impact on average age of accounts. They continue to report for up to 10 years. However, when closed the credit line is no longer available, so if you have balances on other cards, utilization will increase.
Obviously opening the new account does decrease your average age of accounts, and the inquiry will hit your score, but on the positive side, it increases your overall limits helping utilization.
Too late now but it's a good rule not to apply for new things within 6 months of applying for a mortgage. Just be prepared to explain to an underwriter why you got this card. ("I am drowning in debt and need to get any extra credit I can" would not be a good answer, but "It offers very attractive awards for my needs" might be.)
While I am usually very pro closing cards, in this case I would hold off, the fewer changes to your file before the mortgage app (if it really is two months or so) the better.