This is a java version issue: PDB 5 (and PuppetServer 5) requires Java 8. The next package ship should have dependencies which enforce this at install time.
Personally with the APT repo "puppet5-nightly" on Ubuntu Trusty I have not found a "PuppetServer 5" package. There are a "puppet-agent" package, a "puppetdb" package, a "puppetdb-termini" package but the "puppetserver" package is still the version 2.7.2 so no "Puppetserver 5" package unless I have missed something. I make you this notice because I don't really understand when you write "PuppetServer 5 requires Java 8" (I don't understand what is "PuppetServer 5" exactly).
Java 8 is not available on Ubuntu Trusty so a PuppetServer 5 will not be possible (or not possible easily) on Ubuntu Trusty (which doesn't shock me it's just for information).