How to say it in English?

consecutive holidays? which is too wordy i think. Or how about "next week I have 5 holidays in a row".

I'm going to have a five-day holiday.

Yes, I agree with Enigma. "Consecutive holidays" is the formal answer, while "holidays in a row" is more colloquial. Sometimes the latter can be used to denote two or more strings of consecutive holidays in a row, e.g.
two Friday holidays in a row
= two four-day weeks in a row
This is gonna happen in Taiwan soon. When Dec. 25 is a Friday, Jan. 01 is too, and that makes two Friday holidays in a row.

Found in the following search:
http://www.teachersparadise.com/ency/en/wikipedia/h/ho/holiday.html
Consecutive holidays are a string of holidays taken together without working days in between. They tend to be considered a good chance to take short trips, for example. In late 1990s, the Japanese government passed a law that increases the likehood of consecutive holidays by moving holidays fixed on certain day to a relative position in a month such as the second Monday. A well-known consecutive holiday in Japan is golden-week, roughly lasting a whole week.