HeathrowAirport: Connection time between terminals (Dublin)

Would anyone have any info on how to get from Terminal 1 to Terminal 5 in Heathrow Airport London? Any similar experience?

Booked separate tickets Dublin – London (arriving at Terminal 1 Heathrow) and London – Sao Paolo (departing from Terminal 5 Heathrow) - both tickets with British Airways, and have exactly 90 minutes between these flights, provided that AerLingus will be on time in London. From what I have heard from my colleagues at work, it seems that 90 minutes may be a bit tight.

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Any input is much appreciated. Thanks.