You each are eligible for a catchup contribution. Your catchup contribution of $667 ($666 rounded up) added to the family limit of $5,166 equals the $5,833 that you have contributed to you HSA. Your wife can contribute $1,283 plus her $1000 catchup to her HSA for a total of $2,283 to her HSA. The combined total is $8,116.
The $7,449 amount that Opus 17 mentioned is the amount that your wife could contribute to her HSA if all $5,183 of the family limit was allocated to her HSA instead of to your HSA, leaving you with only your $667 catchup that you could contribute to your HSA. $7,449 plus $667 equals $8,116.
