I have a 5v square wave signal being sent from a microcontroller at a baud rate of 115200. I would like to send this signal over longer distances, say 15+ feet. What is the best/simplest approach to ensure this signal is sent cleanly over the longer distance?
Consider using RS485 drivers and receivers and a properly terminated twisted pair. The old SN75176 is one choice- there are newer products.
Assuming you're talking about a unidirectional one-wire type interface, you can use a single pair from Ethernet cable, for example. You can use some or all the other wires for the (required) ground.
You would need a transceiver at each end (you can enable both continuously) and a suitable termination resistor at each end - for CAT5 100 ohm resistors would be better than the usual 120 ohms used for RS485.
Using the above arrangement, a few hundred feet should be no problem.
The 75176 will work with a 0/3.3V input signal from the Tiva so you don't need a voltage translator.