How does an inverting op amp add a DC offset?
The fact that you are using ground as the positive supply is your problem. On the one hand, an op amp cannot possibly produce an output higher than the + power supply nor lower than the -, so hoping for 2.5 from your circuit is a no-go. On the other, in general it can't get all that close to those supplies either. There are exceptions to the latter, called rail-to-rail op amps, but the LT1007 is not one of these. This is why you're only getting -0.6 rather than 0. I'm actually fairly impressed that the LT1007 gets that close to V+. Linear Technology makes good stuff.

The first thing you should do is look at the data sheet. While you aren't an expert in these things, you should notice that the LT1007 is only specified for operation at +/- 15 volts. In fact, you can get away with +/- 12 volts (which is what I recommend). And, depending on the op amp, you can often use even lower voltages - but I wouldn't recommend it in this case. A repurposed PC supply will have +12 available. In a pinch, you could have a go at using +5. Just be aware that if you do, you are operating way below the specified conditions, and if it doesn't work you have no complaint.