The most common and most likely answer to this crossword clue is the 5 letter word GREED
I've seen this crossword clue in The Guardian
G
R
E
E
D
More clues leading to the result GREED
- Excessive desire to have browser — Google’s first up
- Country ignoring church, starting to descend into sin
- What Thatcher might use to pursue grand, selfish desire
- Voracity is permitted, first off
- German stag’s returning appetite
- Consented to give up a vice
- Piggery, rank, old, deserted
- In the end smoking grass produces strong desire
- Piggery‘s good animals from the south
- Accepted going topless is a sin
Buddy explains!

The straight part
We know that "selfish desire" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case selfish desire = greed.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 GREED mean?
GREED noun- A selfish or excessive desire for more than is needed or deserved, especially of money, wealth, food, or other possessions.
- To desire in a greedy manner, or to act on such a desire.