Hi,
Now I have taken a power adapter from my RbPi, it is rated at 2A @ 5.1V, and I have measured it to 5.3V. This is in the green area but I have put in the before mentioned regulator which gives me a nice 4.25V which is will ensure my LED's not burning out too fast - this works very well!
So you have 5.3V feeding the 5V 7805?
The reason you are getting 4.25V out is because 5V input is not enough to give you 5V output that is regulated.
In fact you nay find the 7805 will start to get hot.
Can you please post a copy of your circuit, in CAD or a picture of a hand drawn circuit in jpg, png?
Can you tell us your electronics, programming, Arduino, hardware experience?
Thanks.. Tom.. 