The most common and most likely answer to this crossword clue is the 5 letter word MOULT
M
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More clues leading to the result MOULT
Buddy explains!

The straight part
We know that "shed hair" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case shed hair = moult.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does MOULT mean?
MOULT noun- The process of shedding or losing a covering of fur, feathers or skin etc.
- The skin or feathers cast off during the process of moulting.
- To shed or lose a covering of hair or fur, feathers, skin, horns, etc, and replace it with a fresh one.
- To shed in such a manner.