Here is a way to get access to your F5 and F6 keys, and any other functions keys you want, as Hotkeys. It uses the keyboard remapping application Karabiner Elements.
1) In keyboard preferences, click "Use F1, F2, etc. as standard function keys"
2) Download and install Karabiner Elements. https://github.com/tekezo/Karabiner-Elements
The main application Karabiner does not yet have a version for Sierra. Karabiner Elements provides some of its functionality, including control of the Function keys. If you are running an earlier OS, you might find an older Karabiner application will work.
3) Using Karabiner Elements, set any function keys that you use for Mac things back to their original function. I use the media keys F7 F8 F9, as well as the brightness keys F2, F3 and volume keys F10, F11, F12, which leaves F3, F4, F5, F6 open for use as Hotkeys in Alfred.
4) Any function keys you haven't re-enabled using Karabiner Elements are available as Hotkeys in Alfred. For instance, here I use the F3 key to toggle the wifi.