The most common and most likely answer to this crossword clue is the 5 letter word KARRI
K
A
R
R
I
Buddy explains!

The straight part
We know that "Aussie eucalypt" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case aussie eucalypt = karri.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 KARRI mean?
KARRI noun- The tree Eucalyptus diversicolor, native to south-western Western Australia.
- The hard timber of the karri tree.