USB cable as +5v vcc source
Yes, you can do that, but wouldn't it be neater to leave the cable as is and use a USB socket or plug? Then you just connect the 2 power pins to your circuit.



This plug allows you to enter a common USB cable, and go on from there, connecting wires to just the +5V and ground. Then you're no longer constrained by the limited length of USB cables.

If you do want to cut the cable then usually red is +5 V and black (not brown) is ground, but measure the voltage on the wires to be sure. Make sure that the data wires D+ and D- (usually green and white) are left open.  

Note that USB 2 only allows you 100 mA, and a 10 &micro;F capacitance.