First, save the cheatsheet.gif somewhere on your computer.
On Windows (largely taken from 'How to easily open files and URLs from the [windows] command-line' and 'Execute external programs asynchronously under Windows'), you can use this ex command:
:!start cmd /c start C:\path\to\cheatsheet.gif
To turn this into a keymap, use something like:
:nnoremap <f5> :!start cmd /c start C:\path\to\cheatsheet.gif
To make it permanent, put that line in your vimrc (
:e $MYVIMRC), but don't include the colon at the very start of the line.
:!xdg-open /path/to/cheatsheet.gif &
:nnoremap <f5> :!xdg-open /path/to/cheatsheet.gif &
I can't recall off the top of my head what the OSX command for 'open with default application' is, but the vim command would just replace
xdg-open with whatever that is.
All of these just open cheatsheet.gif with the default program you have set up for GIF images. See
:h ! and (for Windows)