Does that mean that I could replace the new created one (with no version number) by the one name LR5 as exemple and than rename it to remove the version number?
Having LR3 and LR5, two different files, can I check if what is inside LR3 is also inside LR5?
Is there a way to merge different backup?
The name of a catalog can be changed to anything you want. The name does not depend on the Lr version that created it.
Watch this video for some good advice-
Be aware that if you 'open' any 'old' catalog from previous Lr versions, then Lr first copies it and converts the 'copy' to work with the new Lr version (with the addition of -2 to the catalog name). So you will have the new upgraded catalog (containing all the 'old' version info) and the 'old' catalog is left untouched.
I suggest you only have one (and only one) working catalog. All the 'old' Lr3 Lr4 catalogs can be deleted to avoid confusion. (If you continue to re-open 'old' catalogs you are creating many multiple 'new' catalogs.)
Backups are Backups- only to be used when corruption of a catalog occurs and you must restore your 'working' catalog. Merging of backups should not be considered.