I changed it Menu Commands in the preferences, but it still won't work. I tried multiple options in the Actions Options dialog box. Thanks for your help!

Strange. Checked this on Windows 10 with the latest and Beta builds, works for me...
Perhaps some other application steals this particular hotkey for Illustrator? That’s sometimes a case (Skype infamously stealing Ctrl+Alt+Shift+D from Transform Each, for example).
Have you tried other hotkeys?

Also, to see if this is an Actions’ bug or not, test this, please:
1. Remove the assigned hotkey from the action
2. Open Edit > Keyboard Shortcuts, pick Menu Commands instead of Tools
3. Assign Ctrl + F5 to some command you can check, like Edit > Cut or Clear, temporarily
4. See if it works as a command
If it does not — then it’s probably a stolen key’s case. If it does — then something is haywire with actions.

They won't work on the hotkeys that I assign to them. For example, I made an action to open one of my template files, assigned Control+F5 to action and it won't run, but it will run if I hit the small play icon at bottom. I have a Dell keyboard. Thanks

Jim, default actions do not have hotkeys assigned by default, don’t they?
So you mean you try to assign some, and they fail? Which one do you try to assign to which exactly? Is it true for all possible F-keys, for all the actions?
It works fine for me in the latest Beta build. Which one do you try it with?

Default Actions .aia file not letting keyboard shortcuts play custom actions