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

The straight part
We know that "lofty place" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case lofty place = aerie.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 AERIE mean?
AERIE noun- A local chapter of the Fraternal Order of Eagles.
- The nest of a bird of prey.
- Any high and remote but commanding place.