Excellent.

One more question.

I would like to use the arrivals lounge at T3 to freshen up. Would it be possible for me to get to the arrival lounge, then take the Heathrow Express to T5 for the next flight? I understand I will have to go through security at T5 which is fine by me but will obviously save time not having to pick up luggage.

My LAS to LHR flight is Club but LHR to LIN is economy so I won't be able to use the lounge in T5.