What do UK counselling trainees mean by "level 2", "level 3" and "level 5"?

Answer 1

They are most likely refering to the Counselling NVQ level that they are currently studying.

Their approximate academic equivalents are:
NVQ 1 = foundation GNVQ/three to four GCSEs at grades D-E
NVQ 2 = four to five GCSEs at grades A-C
NVQ 3 = two A levels
NVQ 4 = HNC/HND
NVQ 5 = postgraduate qualification