As I know one says the 5 propositions and then goes about his day.
Or are the precepts also pegs for mindfulness? Keeping them constantly in mind?
You have to keep the five precepts constantly in your mind. After while it becomes second nature to you.
Please see this question on Appamada (heedfulness). We need to be heedful of the precepts that we choose to undertake willingly.
This is an idea that doesn't just exist in religion or spirituality.
If you are a professional like a medical doctor, you need to be aware that the life and health of your patients depend on your decisions. If you're a civil and structural engineer designing a building, the lives of the many people who may use the building you designed, depend on your design.
If you have very young children, you need to be always aware of where they are and what they are doing. When you're leaving your house everyday, you need to be mindful of locking the doors, locking the windows and turning off the gas or other heating appliances so that you wouldn't cause accidental fires.
Similarly, you have to be heedful of the precepts that you choose to undertake willingly.
There are also other aspects of the Noble Eightfold Path like Right Speech or Right Action, that we may need to be heedful of.
If you commit yourself to be heedful of practising something, then it should be similar to being heedful of being constantly aware of your very young children's whereabouts and wellbeing. I think it is not very different.
The Five Precepts can be taken formally, but to observe them properly you must be heedful not to break any of the rules during the day. When you break one of the rules, however, there is no need to punish yourself. Keep in mind that you are observing the precepts and strive to improve. This is where being mindful throughout the day of the precepts is important.
One cannot simply be a person who "says the 5 propositions [sic] and then goes about his day" because the whole point of undertaking the five precepts is to follow them and realize the benefits.
Maybe usefull to answer the question: How to Observe(ing) the (5) precepts, Ursula
Keep 5 precepts in mind, first queue, and meditate together. But meditation is second queue.
As time goes by, 5 precepts will be automatically appear in mind. At that time, you just use a few time to check the precepts.
However, if you in a meditation course, you should do follow to your teacher, first. Because (certified) buddhist teacher must can read the practitioner mind. So he should know what is the best for his student.