You mean Photoshop 5.5 which shipped in 1999? Unlikely.
Your options are
- buy Photoshop CS6 (pay full price), or
- buy Photoshop Elements 11 (pay full price), or
- subscribe to the Creative Cloud (and pay a monthly fee).
Or are you talking about CS5.5? In that case probably.
Photoshop cs5 definitely works fine on windows 8 aside from some problems you may or may not have if you have an amd graphics card.
Photoshop 5.5 (1999) Yes it will probably work, but might be a few glitches here and there.
(photoshop 4.01 runs on windows 8 x64 pretty good, but not easy to install the right way because of the 16 bit installer)
ps 5.5 uses a 32 bit installer so it should install normally.
If you have a hard drive 1TB or bigger. then ps 5.5 (1999) won't work and is more trouble than it's worth to get it to work right.
There was no Photoshop CS5.5 but I guess the poster could be talking about the Creative Suite CS5.5.