Early flight from T1 but staying at Sofitel T5 - Transfers ?

Hi all,
Flying to Vienna at 6am from T1 on Friday but we had a great deal to stay at Sofitel T5.
Due to the very early departure, using Heathrow Express to get to T1 isn't an option. I'm getting lost in the jungle of Hoppa Buses and public buses and nothing seems to fit the bill ...
Any idea on how to get from Sofitel to T1 that early ? I assume a cab will be the only option but in that case, how much would they charge ?
Thanks a million in advance !

The N9 London bus runs 24 hours from t5 to Central then a short walk through the tunnel to t1

CHill710, you're the man ! Thanks a lot for this, I will investigate further !!

Absolute genius ! N9 buses run every 15 minutes from Stop nr. 6 at T5 ... That's brilliant and will considerably help us ! Once again CHill710, you're a star, thanks a lot !

Glad to be of assistance.

As a bonus london busses operating within LHR are free of charge.

Glad to be of assistance.

As a bonus london busses operating within LHR are free of charge.

Are they ? Even better ! Good news keep on coming today ! Thanks once again !

[mitchja]

Details of the bus services (including the free ones) around LHR can be found here

As a quick feedback, after using the N9 service between T5 and Central Bus Station, I have to say that it's really convenient. We caught the 3.55 bus and it was perfect, quick and efficient ... And even better, it was free !!!

The N9 can be full of "characters".

(Well it will be now!)

On the day it was just me and my partner ... Not sure we can list ourselves as "characters" but we are happy to oblige