Here is almost the last version mirror of cygwin which supports Windows XP.
Cygwin version: 25 Aug 2016 ('30 Aug' dump is coming)
Setup version: 2.874
(x64 is coming)
Mirror to use: http://cygwin-xp.portfolis.net/cygwin
Run installer with '-X' flag to skip signature verification, because signature file is missing
Thanks to http://www.fruitbat.org/Cygwin/timemachine.html
Contact me: cygwin.portfolis at gmail com