Ugh no. "three sets of things must be present.... Five basic elements: carbon, oxygen, hydrogen, phosphorus and nitrogen."
That would be Earthlife, but there's no requirement they be present for life generally.
It's not like we have any other models right now, is it?
We don't have any current examples, no, but Gerald Feinberg and Robert Shapiro's book _Life Beyond Earth_[1], though published in 1980, gives a variety of provocative suggestions about what life other than earthlife might look like, and how we could detect it.
I think this is why exploring for life on some of Saturn's and Jupiter's moons will be exciting. If there is life on those, especially places like Titan, it will likely be quite different from what we have here on Earth.
Not a lot of complex chemistry to choose from, but organic chemistry.