Praise be to Allah.
The hadeeth is saheeh (authentic).
It was narrated by al-Nasai, 3939 from the hadeeth of Anas ibn Malik (may Allah be pleased with him).
It was classed as saheeh by al-Hakim (2/174), and al-Dhahabi agreed with him. It was also classed as saheeh by al-Hafiz ibn Hajar in Fath al-Bari, 15/3 and 11/345.