You are using a very old version of both CakePHP, and PHP. The easiest way to get faster performance is to upgrade to PHP 7 (You're looking at a 100%+ improvement in performance), disable xdebug on your production system, and ensure that the debug mode is disabled for your application. Also, ensure that you upgrade to the latest version of CakePHP for optimum performance, and security.
From there, you need to start looking at your application. Get some kind of profiling and application monitoring in place, I would recommend blackfire.io for profiling, and newrelic.com for application monitoring. Both are fantastic tools, and offer trials and free plans which should be enough to help you to find the cause of the slowness.
Our large (100 000+ lines of code) CakePHP 3 application has response times of ~180ms, with minimal caching.