The most common and most likely answer to this crossword clue is the 5 plus 5 letter word FAIRY TALES
I've seen this crossword clue in The Sunday Telegraph
F
A
I
R
Y
T
A
L
E
S
More clues leading to the result FAIRY TALES
- Lies lead to Farage, as reality gets distorted
- Lies and falsity are shocking
- Left, as furious about dismissive lies
- Moderate OK about cheers meeting Left’s fibs
- Unbelievable stories are concocted with falsity
- Safety rail adapted for diversions in the nursery?
- Lies concocted as if reality? Not I!
- Calamitous safety rail inventions
- Reasonable having young dogs speaking in children’s stories
Buddy explains!

The straight part
We know that "Unbelievable stories" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case unbelievable stories = fairy tales.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.