No, you didn't show any overpayment on the original return so you wouldn't say that there was one. The IRS will cash your check and then refund it as part of the $5,000 they will owe you when you file the amended return.
You can file both federal and state amended returns at the same time.
Since the IRS has not cashed your check, they may adjust your return automatically, especially if your error is obvious and they can determine it based on the W-2 entry you made, so it may be wise to wait until they cash your check before you submit the amended return.
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