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Um, I'm most sure I'd say за последние пять дней and not за последних пять дней. But I think both variants are possible

As for examples:

The first 4 are okay

The 5th one should be:

Он...

Well, let's try to explain what each time preposition means then. I warn you it might be confusing or not accurate 100%, still it's worth a shot.

За - For me it indicates the continuity of the...

1. We opened two new factories in / during three years = Мы закрыли два новых завода за три года. - Good
2. They have issued the new driving licence in six days = Выдали новые водительские права за...

Я перевел текст за два часа - It took me two hours to translate the text
Я перевел текст на два часа doesn't even make much sense

Он за год изучил русский язык - It took him a year to learn...

Just type за мной in the blank space for this example and it says "правильно"!
But if you type the actually correct за меня it gives you a hint '[in exchange for me]', suggesting that you reconsider...

Боб Уайтман

How could you miss this awful sentence?

When I was sick, he read my paper for (instead of) me at the congress.

The site claims that the correct Russian would be:
Когда я...

Yes, it's true.

На год, неделю, день, час etc.
The same is true for планы на будущее

По этой причине я очень внимательны (because it's plural) внимателен, когда использую русский язык и иногда я предпочитаю не говорить по русский(a typical mistake, we don't ever say по русский...

We say спасибо за + accusative. The rest of your Russian is good

Well, I don't know if there is a rule of when you should use which word. But, what I do know, that these prepositions have different meanings. Let me explain.

Я строю планы для будущего - This...