I agree in principal with TeslaIaint with some minor mods.
A LM7805 regulator is rated at 1 amp which may leave you a bit short. Also being a linear regulator it will put out a lot of heat dropping 2.4 volts at 1 amp and run your batteries dwon sooner by shedding the excess power as heat. Try a switched mode regulator such as this for ~$3 more:
It also gives you an extra 500ma current.
The battery pack in the link is a couple of 18650 LiPo cells, connected in series and sealed into a pack. They cannot be charged individually. When LiPo cells are charged in series they get out of balance over time. On the first charge, because the cells are not exactly the same, one cell gets more charge than the other. The next charge will see the most charged cell gte more of the total charge than the less charged cell. Over time the 'sick' cell will get little charge and the dominant cell will get most of the charge. Eventually the cell pack will effectively deliver the capacity of a single cell as the lesser cell contributes less and less.
Have a look at these LiPo packs:
These have two sets of leads: the thick power out leads and the thinner, multiwire, balanced charging leads. This site also has cheap balancing chargers for LiPo's.
Do not try to charge LiPo's with anything other than a LiPo charger (i.e. not NiMh or NiCad chargers) or they may explode.