Advice on connecting batteries in series
If you connect those batteries in series, you'll get the sum of the rated voltages: 1.24 + 1.31 + 1.3 + 1.27 = 5.1VDC but this is true on unloaded state. 

When the batteries are connected in series, the capacity will be practically the minimum one of the rated capacities, not the sum. Since you claim that each battery has a capacity of 2000mAh, total capacity will be 2000mAh when they are connected in series.

Practically, it can be said that the lifetime will be approximately 2000mAh / 500mA = 4 hours, but please consider the discharge curves. Like the one below:



According to the graph, one battery voltage will be about 1.25VDC for a 500mA load. Then the total voltage will be 1.25 x 4 = 5VDC. If the load current remains constant then the lifetime will be about 4 hours.