Full request question

After five months, I think it's appropriate to politely nudge the agent.

General etiquette, nudge after three months on a full is okay.

You can also check their response times to manuscript submissions on QueryTracker.

Unfortunately some agents do not always send rejections on fulls.

yup I third what's said above, after three months you are totally in the right to send a nudge.
So after five, I would totally be sending that nudge. That's a long time to wait.