What does the 5 in DSM-5 refer to?

Refer to Section 10.2 (example 32) of the APA Publication Manual, 7th edition, and the APA Style website for information on citing the DSM.

Complete work:

American Psychiatric Association. (2013). Diagnostic and statistical manual of mental disorders (5th ed.). https://doi.org/10.1176/appi.books.9780890425596

Text citation: (American Psychiatric Association, 2013)

Individual chapters:

American Psychiatric Association. (2013). Cautionary statement for forensic use of DSM-5. In Diagnostic and statistical manual of mental disorders (5th ed.). https://doi.org/10.1176/appi.books.9780890425596.CautionaryStatement

Text citation: (American Psychiatric Association, 2013)

In-text example:

The Diagnostic and Statistical Manual of Mental Disorders (5th ed.; DSM–5; American Psychiatric Association, 2013) is the most widely accepted nomenclature used by clinicians and researchers for the classification of mental disorders.

The first time you cite the Manual, give its full title as above. After, you can use the abbreviation DSM–5:

The DSM–5’s classification involves a shift from the traditional categorical approach to a dimensional approach. The changes involving the removal of the legal problems criterion and the addition of a craving criterion were retained in the final revision of the diagnostic criteria (American Psychiatric Association, 2013).

You can use the abbreviation APA for the author, as long as you introduce the APA's full name at first reference:

The Diagnostic and Statistical Manual of Mental Disorders (5th ed.; DSM–5; American Psychiatric Association [APA], 2013) is the most widely accepted nomenclature used by clinicians and researchers for the classification of mental disorders. . . . The changes involving the removal of the legal problems criterion and the addition of a craving criterion were retained in the final revision of the diagnostic criteria (APA, 2013).

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