BRP

Hello

So, my BRP Tier 5 is expiring on 15/10/2019. My question is, do I have some extra days for leaving or I must leave before the BRP expires?

Once I left the country after BRP expires, can I come back to the UK the following days as a tourist?

You must leave by the date on your BRP. If you come back a few days later you will have a hard time convincing UK Border Force you're just here for a holiday. It simply doesn't look right.