I would not tap into the fan connection. First off, most of them are not +5, but also +12. Also, most of the fan connections have very limited current capability, and many fans are also speed controlled by varying the voltage.
If you connect the negative leg to the black connection, and the positive leg to the yellow connection of a disk drive connector, you can run all the LED's you can stuff in the case without affecting the operation of the computer. You can easily draw 3-4 amps from that connection, which is enough for several hundred of those LED's.