What is DSM 5 and ICD 10 classification system?
They both are classification systems. In simpler words, these are books in which you can find disorders and their sympoms, based on which a psychiatrist may diagnose you.
The main difference is that DSM (Diagnostic and Statistical Manual for Mental Disorders) was created by APA (American Psychiatric Association) and is used mostly in the US, while ICD (International Classification of Diseases) was written by WHO (World Health Organization) and is used mostly in Europe.
The numbers are just the editions, meaning that the higher numebrs means that the previous version of the book was corrected.
I hope it helps