"hamburgefontsiv" is used a lot because it uses most of the shapes you need to build other letters.

I would look at letters with terminals, like: 'S' and 'C', joins in letters like 'M' and 'A' and – since I need five of them – the question mark: '?'.
'R', 'G', 'Q', 'g' and 'a' are also often treated differently (and probably many others as well).

Ooops. I cheated!

I would pick the first five letters of the font name (preferably in order) - it should be able to guess the font name based on these.

Depends on the classification (serif, sans, display), but generally...

lowercase: g, a, s, o, i, l
uppercase: R, C, G, I, Q, J

This'll help. Thanks frode, sil, Stephen! Appreciate it.

What Stewf said. My pick:
RagßQ

I think it varies from font to font. For example the letters that are distinctive in Minion for me are acjty or MKQR5, whilst in Meta it's aegksy or CEGMS, or in Officina gimty or in Bliss bgyGW.

On the whole I guess I look at:
lc: a, g, e, n, t, (+s)
uc: G, E, M, Q, S.