Micro Usb to HDMI without MHL
To connect your Samsung Galaxy S4 to a TV, you need to use an 11-pin MHL cable. 11-pin MHL cables are usually Y-shaped, and state specifically that they're for Samsung phones.

That's the only way. You can't use a 5-pin MHL cable with this phone. You can't use an app or custom ROM, or any other kind of software on the phone, to get around the need for the right cable.

See How does MHL work? for more information.