Do you have any Oneworld status? If you are oneworld emerald then you would have access to the Galleries First Lounge at T5 and could use the Forty Winks sleep pods.
https://www.flyertalk.com/forum/brit...area-gf-2.html
Otherwise you could try to find a quiet spot in the lounge or see how much a day room might cost at the Sofitel at T5.