The regulation of a uA7805 is guaranteed only when its input is 8V and more. The regulation is spec'd to be much worse when the input is only 7V.
µA7805 data sheet
At 7V with voltage is only going to change by 250mV which is hardly going to cause it to drift a lot.
The specification on the datasheet is with a load current of 1A over the full temperature range, at lighter loads and room temperature, it will be considerably better.
The Texas Instruments datasheet doesn't specify the drop-out at lower currents but National Semiconductors' does.
**broken link removed**
Look at the graph on page 6.
How much current does you circuit use?
An educated guess about 50mA without analysing it in great detail.
At 0A it's 1.5V, at 500mA it's just under 1.75V.
At 50mA it'll be somewhere in between the two.
Interpolating between the two figures gives 1.525V.
The above specifications are at 0°C, at room temperature it'll be a little better.
These are typical figures, if you want the worst case then normalise the figures to those given by worst case specification, like I showed you before.