Join Date: Oct 2006
Location: London, UK
Programs: BA Gold, VS Silver, SQ Silver, IHG Plat Amb, Hilton Gold, Marriott Plat, Accor Silver, Radisson Prem
Posts: 16,871
I don't think you have enough 'comfortable' time to go landside. I would stay airside.
You have to think how long the immigration and customs process takes at T5, then your time in the arrivals lounge, factoring in a maximum 15 minute wait for the HEx at T5 to take you to T1/T3, and then another maximum wait of 15 minutes for the Heathrow Connect to take you to T4, plus the time taken to check in and clear security at T5, and a potentially long walk to the gate in T4.