InDesign CS5.5 does not work with Mac OS X 10.10
What's the last message in the splash screen during startup, if it crashes while the scree is still on?
While CS5.5 is not officially supported on the newest OS versions, it may run OK. Please post your crash report on Pastebin.com and give us a link to it as it may give us a clue. I suspect SING, but we need more info for confirmation.