TE-Common Java Edition
The Java edition currently has the following software run-time requirements:
In order to build the distribution from source, you must have a supported version of the J2SDK along with either 1.5.x or 1.6.x of Jakarta Ant. Obviously, you only need a supported JRE to run applications which use the library.
I have not yet tested any of the TE-Code libraries using J2SE 5.0 ("Tiger"), however, I would expect that it should work.