This is a simple charger circuit which will work for a light load like a DMM, the Battery can be a sealed maintenance free battery of 9V-2AH or better. The circuit will work best if the Unit is powered on many times daily on regular use, else battery will drain down.
Power supply with battery backup - DMM
The 555 Astable is used to generate a AC signal from which a negative voltage is generated, A 79L05 which is a low power TO92 equivalent of 7905 a negative -5 volts regulator is used as -5 volts load is less. A TO220 7805 is used for the +5V supply.
Many dual supplies are derived from one DC Source. A SMPS solution is the best. A Series Regulator is simple to troubleshoot in comparison to Switching Types, there is no EMI-RFI too.
This simple circuit is ok only for Low Current gadgets, Whereas SMPS is green and efficient. In SMPS a greater care for Product Safety is required. In a Linear Supply with Step-Down Mains-Frequency Transformer. The Transformer is the only place, where you look into safety the most. In SMPS it is the PCB, the feedback components and also The High-Frequency (200 kHz) Mains Ferrite Transformer.