From the West End, take the Piccadilly line; estimate around 50 minutes to Terminal 5
https://www.scribd.com/document/1074904087/Private-Hire-and-Ride-Hailing-to-Heathrow-What-to-Know-Before-You-Book-216958
From the West End, take the Piccadilly line; estimate around 50 minutes to Terminal 5, and consider traveling off-peak for a more comfortable journey.