I was loosely following this tutorial to drive some DC motors with an L293D chip via GPIO. Each chip can control two motors each, but what if I want to use 5 motors? I can use 2 chips to control 4 motors, but when I want to add a third chip I have run out of 5V ports, as the Pi 3 has two. Is there any way I can add this third chip? For example, could I take two lines off of one 5V port, where each line is 5V?
The two 5V power pins on the GPIO header are not ports in the sense that ports may be isolated from each other. These power pins are part of a common power bus. There is more than one pin simply as a convenience for multiple plug-in connections (same is true for the 3.3V pins).
As you suggested, you can connect one or more 5V lines to each pin. So two or even three of your chips can connect to a single 5V power pin.
When connecting to the power pins on the GPIO header, you must ensure your current draw is within the available supply of power without causing an adverse voltage drop that might impact other power consumers. Based on the comments above, you are only powering the chips themselves which is not a heavy load so you should be fine as long as your power supply is sufficient.