No, not even close. You can get (at most) 3.3V out of the device with a 3.3V supply and gain of 2.
If you need 5V you can use a DC-DC converter or charge pump to create a higher voltage rail and use a 2:1 op-amp amplifier to double the 2.5V out.
Generally only very special devices (such as those with internal charge pumps and external capacitors) can produce higher voltages than their supply rails, and this is not one of those.
The datasheet perhaps could be more clear on that, by my interpretation, it says that you can get 3.0V out with a 3.3V supply when sourcing up to 10mA. Typically 3.2V (but you can't depend on that). With lighter loading it should be able to get closer to the positive rail.
