I looked in our source code and it doesn't appear that SyntaxEditor handles the F5 key in any way. If you open our Sample Browser application and look at the SyntaxEditor Edit Actions QuickStart, you'll see a list of all the built-in edit actions and they keys associated with them. By default, no actions are associated with the function keys.
SyntaxEditor itself shouldn't be interfering with the key. I did a test of placing a ProcessCmdKey method override on our main SyntaxEditor demo and it hit a breakpoint for the F5 key ok.
If you still think it is a problem with our control, please let us know how to duplicate the issue in one of our samples, and share more about how you are detecting when the F5 key is pressed. Thank you!