Learn Spanish (Spain): Tenemos clase de cinco a siete.

When stating a start and end time using the short structure de ... a ..., Spanish speakers usually drop the article las. However, if you use the slightly longer form desde ... hasta ... (from ... until ...), you must include the articles: desde las cinco hasta las siete.

Why is clase singular here? Could I say Tenemos clases?

You could, but tener clase (singular) is used as a general concept, just like saying "we have class" in English. If you say tenemos clases, it sounds like you are emphasizing that you have multiple different subjects or sessions today.

Does de cinco a siete always refer to time, or could it mean a quantity?

Literally it just means "from five to seven", but when paired with a scheduled activity like having class or working, it is the standard way to express hours. If you needed to clarify that it was in the afternoon, you would add de la tarde at the end.