A couple of points which I don't think have yet been explicitly answered:
--T5 has a fully functioning Tube station where all TfL products can be purchased.
with pedant hat on:
An Oyster card is an electronic payment card which can hold both a "pay as you go" component or a travelcard [of varying zones and durations] or, indeed, both types of ticket. TfL's website says that the purchase of a 7-day travel card requires an oyster card, so that travelcard would be "sitting" on the Oyster card the OP would need to buy at T5 tube station. The TfL site says paper travel cards are available national rail stations. I don't know if the train station at T5 counts as one, or indeed if there are other travel desks at LHR which sell a paper travel card. It's really a moot point as the OP would need to buy a Oyster card to put some PAYG funds on it so he/she might as well just put the travel card onto that Oyster as well.
-- you can get from T5 to T123 via the HEX which is FREE between terminal stations at LHR. This may be quicker than getting one of the buses between the two terminal areas.