The most common and most likely answer to this crossword clue is the 5 letter word LUPUS
I've seen this crossword clue in The Times
L
U
P
U
S
Buddy explains!
The straight part
We know that "Possibly, first Roman wet nurse/disease" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case possibly, first roman wet nurse/disease = lupus.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 LUPUS mean?
LUPUS noun- Any of a number of autoimmune diseases, the most common of which is systemic lupus erythematosus.