Sorry, but that is the only correct actions for this case.
SB-600 does have the Nikon AWL wireless remote feature, for use with cameras that have the Commander. D5100 does not have a Commander. D7100 does, for example.
You could add a commander on the D5100 hot shoe, either a hot shoe flash that also has a commander in it (SB-700 is one), or the Nikon SU-800, which is a Commander-Only model ($250).
These choices still do not give you the FV Lock feature, that cameras with Commander have, and it is pretty important to have (to prevent taking pictures of the subjects blinking). SU-800 is a big improvement though.
Or, you could use Manual flash mode (where it is you yourself that sets the flash power level setting every time).
There are various ways to trigger such a remote manual flash.
1. PC sync cord
2. Optical slave
3. Radio trigger
The SB-600 does not have 1 or 2 (some flashes do), but both are very inexpensive options to add on its foot, so that it does these.
For 1, D5100 also needs an inexpensive hot shoe adapter to add a PC socket. Nikon AS-15 is an excellent one.
For 2, the D5100 internal flash in its MANUAL mode, set to very low manual power, would trigger the remote slave. Or any light in a multiple group could trigger the others, and you trigger this first one any way you choose. All studio flash units include this optical slave.
Radio triggers are available both inexpensive and expensive. This is a little transmitter on the hot shoe, and a receiver on the flash(s).
How to trigger speedlights Off camera has more trigger info, if interested.