You may have to file a New York non-resident return (I assume that you are a non-resident). New York says,
"You have income from a New York State source (see Nonresidents: New York source income) and your New York adjusted gross income (Federal amount column) is more than your New York State standard deduction. Complete Form IT-203, lines 1 through 31 and compare the line 31 Federal amount to your standard deduction from the New York State standard deduction table."
The rule describe above means that a lot of taxpayers who are non-residents might be surprised to fine that they are required to file a New York return, because of the somewhat unusual way that NY taxes people.
Unfortunately, TurboTax cannot help you with the 2018 NY tax return, because our available software does not go that far back.
I suggest that you find a CPA or an Enrolled Agent who is familiar with NY tax law, and ask them to contact the NY Department of Taxation and Finance on your behalf. While it may be true that you were required to file a return, it may also be true that New York State won't get anything out of you filing a return, and this is something that your representative can point out. Your representative can also suggest that waiting 5 years to contact you is too long, given that normally, New York returns cannot be file for a refund after three years (note: the tax department can demand that you file a past due return, no matter how long it has been).
Your representative can also explain to you how NY and NJ avoid double taxation (this is in reference to "taxing me twice").
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