
der Fünfer
fiver
A coin or banknote worth five currency units, especially five euros.
Hast du einen Fünfer für den Parkautomaten?
Do you have a fiver for the parking meter?
fiver
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fiver
A coin or banknote worth five currency units, especially five euros.
Hast du einen Fünfer für den Parkautomaten?
Do you have a fiver for the parking meter?

grade five
The school grade 'mangelhaft' (poor; grade 5), which in Germany and Austria means that the performance was not sufficient.
Leider habe ich in der letzten Matheprüfung einen Fünfer geschrieben.
Unfortunately, I got a grade five on the last math test.

the five
The digit or number five, often used to refer to a public transport line or a number in a sequence.
Der Fünfer fährt nur alle 20 Minuten.
The five only runs every 20 minutes.
'Fünfer' (fiver/five) is derived from the number 'fünf' (five). The ending '-er' turns the number into a noun that refers to something connected with that number.
Gib mir bitte einen Zehner, dann bekommst du zwei Fünfer zurück.
Give me a tenner, please, and you'll get two fivers back.
The word 'Fünfer' (fiver/five) is used mainly in colloquial language in all its meanings. It is a short, everyday form for 'Fünf-Euro-Schein' (five-euro note), 'Note 5' (grade 5), or 'Linie 5' (line 5).
Ich nehme immer den Fünfer zur Arbeit.
I always take the five to work.
The context makes it clear which meaning is intended. If it is about money and paying, it means a coin or banknote. In connection with school and grades, it is a school grade. With means of transport, it refers to a bus or train/tram line.
Ich habe nur noch einen Fünfer im Portemonnaie.
I only have a fiver left in my wallet.
In the context of school grades, 'Fünfer' (grade five) is often used with verbs like 'bekommen' (to get), 'kriegen' (to get), or 'schreiben' (to get/write on a test).
Ich habe hart gelernt, um keinen Fünfer zu bekommen.
I studied hard so I wouldn't get a grade five.
five
Both words can refer to the German school grade 5. “Fünf” is the direct, neutral term for the number or grade. “Der Fünfer” is the colloquial noun form for this grade. “Fünf” is usually more appropriate in a factual conversation, while “Fünfer” is also used in casual speech.

Für diese Arbeit bekam sie einen Fünfer.
She got a grade five for this assignment.
Für diese Arbeit bekam sie eine fünf.
She got a grade five for this assignment.