Could I be angry all the time from a head injury 5 years ago?

Yes. Head injuries can cause personality change and emotional distress.
Post trauma syndrome. Common long term consequence of head injury includes mood disorder. In addition, headaches, dizziness, poor sleep, depressive reaction, poor concentration, etc. These issues need to be addressed by your doctor. Counseling may help and at times mild tranquilizers or mood stabilizers may help. Good sleep patterns are important.
Traumatic Brain. Yes. This may be a persistent sign and symptom of previous traumatic brain injury. Is this definitely different than you were prior to the injury? Many other things can cause anger not related to the injury.