24V DC to +5V and -5V
The most simple solution is to buy a small DC/DC converter with bipolar outputs in an oversized 24-pin DIP package.  Note - these usually require additional capacitors on the input and outputs.

If you want to grow it from scratch, I would go with a linear regulator for the +5 V (because the total load current is so low) and a non-isolated buck-boost converter to turn the +24 V into -5 V.  There are dozens of parts to choose from for this, including ones with the power transistors on-board.  Linear Technology (now a part of Analog Devices) is a good company for this.