Holborn-T1 takes 1 hour (officially). Add a 5 minute walk either end and you arrive at 1:10 door to door, as you calculated.
What you haven't factored in is a wait of up to 10 minutes for a train and the fact that the Piccadilly Line journeys always take around 10 minute longer than they should do. So your 1700 departure will realistically get you to T5 by 1830. That gives a 5 minute buffer. Not something I would be comfortable with.
Leave earlier, or take the HEX.