The most common and most likely answer to this crossword clue is the 5 letter word DOWNS
I've seen this crossword clue in Financial Times
D
O
W
N
S
Buddy explains!

The straight part
We know that "swallows" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case swallows = downs.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 DOWNS mean?
DOWNS noun- A negative aspect; a downer.
- A grudge (on someone).
- An act of swallowing an entire drink at once.
- A single play, from the time the ball is snapped (the start) to the time the whistle is blown (the end) when the ball is down, or is downed.
- (crosswords) A clue whose solution runs vertically in the grid.
- A downstairs room of a two-story house.
- Down payment.
- To knock (someone or something) down; to cause to come down, to fell.
- To lower; to put (something) down.
- To defeat; to overpower.
- To disparage, to put down.
- To go or come down; to descend.
- To drink or swallow, especially without stopping before the vessel containing the liquid is empty.
- To render (the ball) dead, typically by touching the ground while in possession.
- (pocket billiards) To sink (a ball) into a hole or pocket.
- (especially southern England) A hill, especially a chalk hill; rolling grassland
- (usually in the plural) A field, especially one used for horse racing.
- (chiefly in the plural) A tract of poor, sandy, undulating or hilly land near the sea, covered with fine turf which serves chiefly for the grazing of sheep.
- Soft, fluffy immature feathers which grow on young birds. Used as insulating material in duvets, sleeping bags and jackets.
- The pubescence of plants; the hairy crown or envelope of the seeds of certain plants, such as the thistle.
- The soft hair of the face when beginning to appear.
- That which is made of down, as a bed or pillow; that which affords ease and repose, like a bed of down.
- To cover, ornament, line, or stuff with down.