I've seen a number of Hangul syllables that contain 4 characters (닭, for example) - is it possible to have syllables with 5 (or even more) characters in them? The Wikipedia page on Hangul suggests it's possible, but doesn't give an example - and I can't find other resources to say for sure either way.
Old Hangul (옛한글) apparently allowed up to 9 jamo in a single block. I am not sure if this was "proper" use or abuse of Hangul at the time... I managed to find a reference to one of these "in the wild:" ꥸᅦퟗ which cites this document from 1922.
Unicode supports Old Hangul, if just to study and document old Korean texts. (Interestingly, the character ꥸᅦퟗ is rendered as a single character in HTML, but appears as three separate characters in the text box while editing.)
Some special IME's support Old Hangul input. Here is an explanation of how 9 jamo can be combined into a single block: