With Windows I work with inDesign 5.5 and now I have to upgrade Version3. on Mac also to 5.5 and I cannot find how
There is no upgrade path from InDesign CS3 to CS5.5.
Adobe only sells the perpetual version of InDesign CS6 at full price. Unfortunately, that version is 3-1/2 years old, and will never be updated:
A better choice would be to get a subscription to Adobe Creative Cloud for InDesign which will always be up-to-date. I would allow you to install one subscription on two computers—which can include both your Mac and your Windows computer.
If you work with InDesign 3, that is InDesign CS(1), but I suppose you mean InDesign CS3.
Both are very old, no upgrade path exists any more, you can buy (not upgrade anymore) CS6 which is also very old and has also reached EOL, End Of Life and will not be updated any more or you can subscribe to CC, there are several plans available.