The biggest problem I see in your question is that your boss told you about your raise in an email.
I have always done performance reviews and their subsequent salary reviews as an in-person task. And certainly with some explanation.
Prior to this email, had you and your manager done any kind of performance appraisal? If not, that's probably the place to start.
I would set up a face-to-face with your manager to discuss the raise/performance.
You need to understand your goals for the meeting. My goals would be:
- Understand WHY the company offered this amount.
- Ensure the company is aware of the work I'm doing/value I'm adding.
- Initiate a performance review process. It doesn't have to be official, but make sure your manager understands all the great work you're doing. (regular meetings every 3 - 12 months to set goals and evaluate your progress)
- Negotiate a higher raise.
Before the meeting, you want to prepare. Document your accomplishments for the past year. What did you accomplish? How did you go above and beyond? What are some examples where you did more than was asked or expected of you? These are why the company should value you.
If you can't come up with a decent list here, be satisfied with the 5% and focus on setting goals and reviewing them regularly with your manager. Your personal goal for next year would be to have a nice list of accomplishments.
You should start the meeting by explaining that you were a bit surprised by your raise this year. You understand that huge raises aren't sustainable, but you felt like you had another really good year.
Then ask for the company's thinking behind the raise.
If your accomplishments aren't being mentioned or are being downplayed, this is when you would break out your listing of accomplishments. "These are some of the things I did this year that I was really proud of and I think demonstrate my growth and added value."
Edit to add:
I would not see this as a "we don't like you and want to fire you!" event. You don't give 5% raises (an above average raise btw) to people you're wanting to let go. You give $0.
The biggest thing you want to avoid is coming off as ungrateful or unreasonable. Avoid statements like.
When I started I was very low on the salary range for my position, and it is still below the average.
That may be true, and there are certainly times to bring that kind of statistic up. I don't think this is one of them. Keep the focus on the good work you're doing and the value that brings the company. There is a range of salaries because there is a range of skills, experience, and value that folks with that title bring to the table.