Yes, definitely get out of the airport with a layover that long. The Peak is an easy 10 minute walk from the train station at Central. Head up on the funicular and have a wander around at the top enjoying the views. Head back down and catch the ferry over to Kowloon around sunset (5pm in HK this time of year).
Get some dinner around Nathan Rd (or there are western options in the big shopping centre if you’re not a fan of the local fare) and soak up the lights of the city before getting back on the train at Kowloon by 8-9pm.
Or if you don’t want to go into the busy centre then take the cable car up to the Big Buddha which is right by the airport. Take a bus to Tung Chung (it’s only 4-5 minutes from the airport) and there is plenty of signage to the cable car terminal. Nice area to get some exercise and some fresh air (by Chinese standards!), also wander through the monastery. There are local food options or lots of western places in the big shopping centre at the bottom in Tung Chung.
As for jet lag, you want to spend as much of the flight as possible asleep. Have an active day and get on the plane tired. Drink plenty of water (if you’re on Cathay then they will have big trays of water/juice set up in the galley for you to help yourself to) and I also take a small tube of moisturiser (under 100ml) to apply every couple of hours because I get very dried out on long flights.
And most importantly, stay awake as long as possible on your first day in the UK. No naps, they will turn into proper sleeps and you’ll spend the night awake. Have a quiet morning then have a shower, put on some fresh clothes and go out for a few hours. Five weeks is heaps of time though so it’s not a big deal if it takes a week to adjust. Just take it as it comes.