Final answer:
Gender Dysphoria is the DSM-5 diagnostic category for individuals who do not identify with their sex assigned at birth and experience significant distress or social impairment as a result.
Step-by-step explanation:
The diagnostic category in the DSM-5 that refers to individuals who do not identify with the gender that is typically associated with their biological sex is Gender Dysphoria. Gender Dysphoria encompasses those who feel a significant incongruence between their experienced or expressed gender and the gender others would typically assign to them based on their biological sex. This condition must cause significant distress or impairment in social, occupational, or other important areas of functioning and persist for at least six months for a diagnosis according to DSM-5 criteria. While not all transgender individuals experience gender dysphoria, this diagnostic category ensures that those who do have access to necessary medical and psychological support.