If your talking about photoshop 5.5 from circa 1999, then it should install and run on windows 7, as long as you don't have 1 TB or more of free space on your c drive
How can I upgrade Photoshop 5.5 from Windows XP to Windows 7?
R_Kelly's got you covered if you're talking about the original version 5.5. However, if you're talking about Photoshop CS5.5, you'll need to deactivate it on your old system, then install it and activate it on the new one.
Better yet, get the business or ultimate edition of Windows 7 and you can install XPMode, which I tested at work and it's pretty slick. Basically, XP mode (once installed) becomes a Start menu option, kicking off a virtual XP session. Any programs (such as Photoshop 5.5) you install in XP mode will also find their way on your start menu (under XP-mode) so you can luanch that XP program without having to first launch XP mode. Handy. Can't say if it will work with your specific program (nor am I saying Windows 7 can't run Photoshop 5.5) but it's something to consider, perhaps.