The air-side bus is the easiest method as it does not require you to re-clear security which is somewhat unpredictable. I believer the bus starts running at 11:30am each day. The bus station in T5 is at gate M13. T1 is at Gate B1. There is a stop in the high G-gates and, I think, K gates. The G/K bus is a separate bus from the B bus. If you allow 30 to 35 minutes for the bus you'll be fine.

The land-side train is faster, at least to T5. Whether or not it is faster gate-to-gate will depend on how long it takes to re-clear security at T5.