If any program is capable of converting / exporting / saving .br3 files to .b5 files is the Bryce software from which both originate. It is likely the latest version of the program still supports its previous formats and can somewhat transfer one to another. If not, there is probably no other way how to do it.
Convert Bryce version 3 scene file to Bryce version 5 scene.
We have found 2 software records in our database eligible for .br3 to .br5 file format conversion.
Microsoft Windows software - convert br3 to br5 on Windows
A graphics design tool for making 3D landscaping and animations
Convert from br3 file format
The tables with software actions are a good pointer for what a certain program does with various file types and often may give users a good hint how to perform certain file conversion, for example the above-mentioned br3 to br5. However, it is not perfect and sometimes can show results which are not really usable because of how certain programs work with files and the possible conversion is thus actually not possible at all.
Apple macOS / Mac OS X software - convert br3 to br5 on OS X
3D modeling and animation package for Mac.