Even if a serial number works, you will be stuck with the 2015 version. You will miss critical security patches, driver updates for new burners, and compatibility fixes for modern video formats (HEVC, AV1, etc.).
If you bought a digital download from the Nero web store between 2014 and 2016, search your email archives for "Nero order confirmation" or "Your Nero serial number." Log into your My Nero Account – legacy purchases are often stored there. nero 2015 serial number