The most common and most likely answer to this crossword clue is the 5 letter word SPERM
S
P
E
R
M
Buddy explains!

The straight part
We know that "a member of the whale family" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case a member of the whale family = sperm.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 SPERM mean?
SPERM noun- The reproductive cell or gamete of the male; a spermatozoon.
- Semen; the generative substance of male animals.
- Sperm oil; whale oil from a sperm whale; spermaceti.
- To ejaculate.
- To ejaculate on or into.