Assuming you mean CS5, all versions of Lightroom are compatible with it, but some versions are more compatible than others.
If you want to transfer RAW images from LR to CS5 for further editing, I believe you need Lightroom 3, but all versions of Photoshop can work with TIF or PSD generated from any version of Lightroom.
Hi alans 25,
Lightroom Version 3,4,5 and 6 / cc all are compatible with Photoshop CS5.5
But it will give you error messages like: "Lightroom may require Camera Raw X.X for compatibility". or you might would not be able see some edits which are not there in the version of camera raw you have in Photoshop CS 5.5
Please check the following list of Camera supported with the version of camera raw required in Lightroom and Photoshop :
Please let us know if helps