The actual upgrade went fine and there were no problems starting Eclipse or compiling code in Eclipse afterwards. Eclipse had automatically detected the new JVM and updated the JVM for the various projects. I kept getting errors saying “Specified VM install not found” when trying to launch Ant build files though.
After Googling a bit most other posts discussed launch configurations so I checked the launch configuration for the build files and there it was… For some reason the JVM isn’t automatically updated for launch configurations. Worth noting.

Selecting the 1.5 JVM from the list solved the problem.