Despite claiming support for JIRA 4.3 up, the latest UPM will not install on 5.0.7 (old I know but there you go). I don't mind if it's truly unsupported, but the documentation should make that clear if so.
Error is:
Caused by: org.springframework.beans.factory.CannotLoadBeanClassException: Error loading class [com.atlassian.upm.selfupdate.async.SimpleAsyncTaskManager] for bean with name 'simpleAsyncTaskManager' defined in URL [bundle://124.0:0/META-INF/spring/atlassian-plugins-components.xml]: