I've been going through the HSK lists with awk, so I now feel like I can answer...
Question: What are the HSK chengyu (idioms)?
My answer is below.
To my knowledge, there's no HSK5 idioms, except possibly 讨价还价 (to haggle over price), but I don't think that counts. This is not to say there's no requirement to learn idioms for HSK5, but that it's not on the official list.