The most common and most likely answer to this crossword clue is the 5 plus 3 letter word WHITE LIE
I've seen this crossword clue in Independent
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More clues leading to the result WHITE LIE
- One embraced by former Countdown host, short and a little porky
- We relax, consuming punch and a mini pork pie?
- Scrap with priest over English falsehood
- While it circulates before start of election, it’s not true
- No BAME person would spin such a harmless story
- Justifiable deception as we don’t stand up about strike
- Prevarication – it’s the middle-of-the-road thing, not new
- It’s not a colourful story?
- Woman's upset with priest joining leading evangelist to deliver frivolous fib
- We are prone to absorb blow as harmless deception
Buddy explains!

The straight part
We know that "falsehood" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case falsehood = white lie.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.