Problem with using comparator to amplify signal
The LM293 is only guaranteed to be able to sink 6mA. You have a 100 ohm pull-up resistor and with 6mA flowing into the chip's output, the output voltage will be limited to not going below 4.4 volts. Using a typical output current sink value of 16mA, your output might be able to pull down to about 3.4 volts and you may get a shade or two lower.

If you made the pull-up resistor more like 1kohm you'd be a bit better off but, then you are going to have problems reaching the 5V rail. Either compromise your requirements, use a higher supply voltage or consider using a rail-to-rail output device. 

However, even with a rail-to-rail device, the output will clip at about 4.9 volts and 0.1 volts from a single 5 volt rail.