Surely the cheapest solution is to flirt outrageously with your elderly neighbour and in so doing get her (or him) to open their big drum for your regular gratification. An occasional bag of washing aids may be all they expect from this 'neighbours with benefits' arrangement.
Avoid '5 á sec', they're expensive and not in my experience very good. There are decent drycleaners on both ul. Hoża and ul. Wilcza. As a rule, for drycleaners in Poland, the oldest are the best (and cheapest), the worst are in shopping malls or ones with 'eko' in their name.
If you happen to be in Zoliborz, there's an excellent one on ul. Promyka behind the flats. They mostly do contract work (restaurant tablecloths, hotel upholstery etc) but not only. That's the one I always use and they shift stains that '5 á sec' doesn't (at less than half the price). I can strongly recommend them.