This article explains how to connect a PS4 to a TV without an HDMI port using an HDMI converter or an HDMI to DVI converter.
How do I connect my PS4 without HDMI?
One of the most effective and easiest ways to use a PS4 and a TV without HDMI is to use an HDMI converter. This translates the signal into something that the TV can understand and display. That said, there are different types of HDMI converters, so you'll need to determine which type you need.
Check the connections on the back/side of your TV.
This could be anything from a coaxial input, a DVI input, composite cables, or one of many other options. A coaxial input looks like a threaded screw. Composite inputs are three ports for red, white, and yellow cables. A DVI input looks like what older computer monitors used to connect to.