Increasing input signal by 5V (Using 7805 voltage regulator)
If I understand you correctly, you are trying to adjust the output voltage of your 7805 regulator to output 5V - 10V by adjusting the voltage at it's ground pin between 0V and 5V.
If you are doing this, the pin needs to be able to sink current in order to maintain regulation, so whatever the power source used, it needs to be capable of this. Many supplies will only source current, and if this is the case what you are seeing will occur.  

A simple resistor divider with potentiometer can be used, or an opamp to drive the 7805 ground pin is maybe the best solution, preferably with a output including its negative rail if you want to go all the way down to 5V. You will find many example adjustable supply circuits on the web, and in the datasheets of the regulators also.   

Here are a couple of example circuits:

Pot adjust, from this page with more info:



Opamp adjust, from datasheet pg.24 (don't use a 741 if you can possibly avoid it, as they are obsolete):