fünf
five
The cardinal number that follows four; the numeral 5.
Ich habe fünf Äpfel gekauft.
I bought five apples.

five
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five
The cardinal number that follows four; the numeral 5.
Ich habe fünf Äpfel gekauft.
I bought five apples.

In the German school system, 'eine Fünf' (a five) is a bad grade. The grading scale ranges from 1 ('sehr gut' — very good) to 6 ('ungenügend' — insufficient), and a 5 means 'mangelhaft' (poor), i.e. failed.
Ich habe Angst, dass ich in der Prüfung eine Fünf bekomme.
I'm afraid I'll get a five on the exam.
The idiom 'fünf gerade sein lassen' means to be lenient or not apply a rule quite so strictly. It is commonly used in colloquial language.
Normalerweise dürfen wir das nicht, aber der Chef hat heute mal fünf gerade sein lassen.
Normally we're not allowed to do that, but the boss was lenient today.
Another common idiom is 'fünf vor zwölf' (five to twelve). It means that it is almost too late and one must act immediately.
Wir müssen die Tickets jetzt buchen, es ist fünf vor zwölf!
We have to book the tickets now; it's five to twelve!
fifth
'fünf' and 'fünft' are both connected to the number 5, but they have different jobs. 'fünf' names a quantity: five people, five euros, five minutes. 'fünft' is an ordinal number and names a position in a sequence: 'der fünfte Tag' (the fifth day), 'die fünfte Etage' (the fifth floor), 'das fünfte Kapitel' (the fifth chapter). Learners may confuse the words because they look similar. Just ask yourself: Is it about the quantity? Then use 'fünf'. Is it about the place in a sequence? Then use 'fünft' with the appropriate ending.

Im Wartezimmer sitzen fünf Personen.
There are five people sitting in the waiting room.
Unsere Wohnung liegt im fünften Stock.
Our apartment is on the fifth floor.