It seems the database format changed between MailStore Home (MSH) versions, and the portable version can't read the old database. So here is how I did it:
1. Note where your version 4.x database files reside on you hard disk -- if using the portable version it should be a folder named 'Data' inside your portable MSH installation folder;
2. Copy the whole folder to a different location -- dragging and dropping while pressing the 'CTRL' key will easily create a renamed copy alongside the original;
3. Download and install the new version of MSH (v5.0.1 at the time of writing) -- you have to install it to your computer, not just make another portable copy of it, although you can uninstall this after converting the database files to the new format;
4. Open the Windows 'Start' menu, navigate to the MSH program group, and launch 'MailStore Home - Select Data Directory' entry; click 'Choose Archive...', point it to the folder created in step 2, and it will start converting the database files to the new format (wait for it to finish before proceeding to the next step!);
5. Run again the installation executable from step 3. and create a new portable copy, taking care to remember where it's at;
6. Copy the folder created in step 2. to the location of the portable MSH created in step 5. and rename it to Data -- run this MSH version and you'll notice that your archive is now available; you can now delete and unistall all other versions, if you wish to...