NY Bank has account holder with last known address in NJ - dormant savings account - do funds get remitted to NJ in 3 years (under NJ law) or 5 years (under NY law)?

AND, is there a penalty that any state would impose if we were to escheat the funds a few years after the required escheatment date?

Funds are escheated using last known address in NJ (3 years).

Penalties:
If you fail to file full and complete reports or affidavits the statute requires in the manner the Comptroller prescribes, you may be subject to penalties and/or late interest as Section 1412 of the statute describes. Willfully filing false reports or making false verification is punishable under the provisions of the penal law.

Interest Charges for Late Payment or Delivery of Abandoned Property
If you are late delivering abandoned property, New York State can charge you late filing interest. Interest is 10% per year from the date payment or delivery was due to the date you make payment or delivery. Interest on securities is based on the closing price of the securities, as of the tenth day of the month in which delivery was due. Refer to Section 1412 of the statute.

Here’s the link to the NYS Abandoned Property Handbook:
http://www.osc.state.ny.us/ouf/oufhandbook/handbook.pdf
(The above penalties section appears on page 13)