Both are correct. It only depends on what you'd like to emphasize.
Your first one is the more common sentence structure (subject - verb - object). You would normally want to use that.
You may prefer to use the second one (object - verb - subject) if the part "Fünf Personen" is the most important information that you aim to convey, and the rest of ...
In this case you can translate "I will not surrender" word by word -> "Ich werde nicht aufgeben".
With "mich" you change the meaning by adding "myself". Your answer translates into "I will not surrender myself" or with better wording "I will not give up on myself".