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There are many summer schools or courses which are at least 5 nights long, and you can learn things at the same time too. This can also be an asset to your personal statement if you do something related to your intended course of study, e.g. Medlink for Medicine, JACT summer schools for Classics, etc. They will probably have some information on some courses that could be useful for you, and some teachers even teach also at these events! There are loads of great volunteering opportunities wherein you can fulfill your requirements for the Residential section and do some good at the same time. You could go abroad and help with a project, like building a school, or look for some smaller projects, again like with the elderly or the disabled. You could also see if there's a school/scout/guide group that wants to do something like a summer camp who would appreciate your assistance. If you don't find anything related to your academic interests, or you don't have any especial academic interests, search online for fun things you could do. There are many many places that offer week-long activity residentials, e.g. The National Trust, so search around until you find something that catches your eye.
Go on a course. Ask your teachers for ideas. Do some volunteering. Research online.