There is a little confusion @rahularyan Here minimum PHP Version is 5.3 (https://anspress.io/documents/?doc_page=requirements) And, here minimum PHP version is 5.5 (https://anspress.io/document/requirements/)
Yes its possible. Simplest way is to activate WordPress network and activate Askbug and AnsPress in a child site. Or you can use this plugin: https://wordpress.org/plugins/jonradio-multiple-themes/ and activate AskBug only in AnsPress page.