I use forememory instead of foresight, due to how the ability works.
A cunning and creative person can remember five minutes into the future, and are smart enough to exploit it in any way possible. For simplicity, I will name the person "Abe". They are the only one with this ability, so others seeing the future and changing it won't be a problem. Recalling the previous five minutes and recalling what occurs in the next five minutes are exactly the same for this person. They could spend a few seconds remembering, then take action upon this. Why can't they abuse their power by reiteration (write a note, see his future self writing the note, repeat until two minutes foresight can be five years foresight)?
Abe's five minutes forememory are of what will happen if he didn't remember the future. The act of remember automatically changes the future. However, since the forememory shows Abe what happens if he didn't use the ability, he can do reiteration: If Abe "remembers" nothing happens, Abe doesn't need to take action, but if he makes a warning to his past self, his past self will change their actions, because Abe changed what he did. One possible result is that as soon as Abe can use this power, Abe gets warnings of the future regardless of what he does. This is one reason why I want to "disable reiterations" (although, it would be an interesting story where a person can warn their past self, and the story is how every action they take they still regret their life and warn themselves).
What is reiteration? Skip this last paragraph if you already get it and don't want my clarification of what I envision the ability to be. If you say "pencil" and wait a minute, you will have little difficulty remembering what word you said. It will also take you only a few seconds to remember this. Then, you say the word you remember to a friend. The friend won't have memory of what you originally said (like Abe can't remember 10 minutes ahead), but can remember what you just said (like Abe remembering 5 minutes ahead). This can be "reiterated" until you have a chain of any number, as Abe can do to remember into the future of any distance. In the case of Abe, he can do a similar process. Let's say nothing interesting happens to him for a few hours, but he vigilantly uses his forememory just in case during the whole time. Then, an ambush happens and he is trapped. The ambushers plan for his ability, and wait 5 minutes after blocking all escape routes before revealing themselves. Abe remembers the future out of habit, and notices future Abe getting hit from behind, just like you might feel pain in a memory. Abe quickly writes "Ambush 18:41" on his palm with a marker always kept in his pocket or nearby. Now, the story changes: Abe has nothing happen for a whole week, but vigilantly uses forememory and notices his future Abe writing down "Ambush 18:41". This is because the forememory shows what will happen if he didn't use the ability. What would happen is that he writes the warning on his palm as soon as he knows. Since Abe can see the warning 5 minutes in the past, and the warning is made 5 minutes before the event, Abe has 10 minutes preparation. If Abe writes a warning of the warning "Ambush 18:41" on his palm, the previous him gets 15 minutes of time. Reiterated, Abe could go until the moment Abe woke up that day. If Abe is willing to sacrifice sleep and only sleep 4 minutes at a time, he can sleep 4 minutes (with a loud alarm), then use a minute to check the future and write down a warning on his palm if necessary. If Abe ever fails to keep this chain working (like waking up late), Abe will notice this with the futurememory, and take action to correct it. Note: 18:41 is military time 6:41pm. If Abe desired, he could also write the date instead, or use an extra five seconds for more information if needed.