If you ignore the -5V source and the 1k resistor connecting it to the op-amp's inverting input you've got an amplifier with a gain of -2 (Rfb/R1 = 1000/500 = 2, and it's inverting, so -2) . Putting in an AC signal with a range of 0-5V would give you 0 to -10V on the output. Then, ignoring the AC source and the 500R resistor, and just taking the -5V and the 1K resistor, we have an amplifier with a gain of -1. So -5V in gives 5V out. Now it's a summing amplifier, so we sum 0 to -10 with 5, to give us 5 to -5V. To make it work as a summer you need to ground the non-inverting input so that the feedback forces the inverting input to 0, giving a virtual ground there.
There's probably other ways to do it, but that's how I would go about it.
Cheers