You need to sleep 7 to 8 hours, even if you are not training. You need to prioritise your sleep if you are only sleeping 5 to 6 hours, that isn't enough. Studies have shown the health consequences of sleep deprivation are serious.
I think somewhere around 7-9 hours would be best; after a long day of training your muscles will need some time to rest/repair itself. On top of that, your kidneys need rest as well from taking in all the food you eat during the day.
You're right, your whole body needs to recuperate and the best time for recuperation is during sleep. People who do not do high intensity training need 7 to 9 hours and the need for sleep is even more important for people who train because this is when your muscles recover and grow.
Sleep is something I think varies with each person based on body size and natural makeup. I think other factors will probably be how much you use your brain. A lot of people think that sleep is all about the body but in reality it's more about the brain. The brain is the thing that is powering your whole system as well as making decisions, thinking, solving problems, experiencing pleasure, pain and so on. Based on that I may need only 6 hours one day to be fully refreshed when I haven't been steward out but I may need 10 hours on another day that has been particularly challenging. On average I try to get a minimum of 6 hours and I feel best after a maximum of 9. More hours often results in headaches and lethargy
I don't think it does vary from person to person, everyone needs at least 7 to 8 hours of quality sleep. There will be health consequences in the long term if you are only sleeping for 5 to 6 hours a night, that applies to everyone.
I would say the magic number is 8 hours every night. Although you may seen fine at first with 5-8 hours I feel that eventually it will catchy up with your health. Our body doesn't always tell us when something is wrong but you will definitely realize that you are harming your health in the long scheme of things. Set a time and try to get that hours. Don't try to cheat health.