+1 Henry's answer. For an alternative approach, rely on the elements of structure; the three act structure specifically, and pace your writing accordingly.
Use 30% for the first act. 1500 words.
You need to introduce the world and your main character (MC): 5% to 10%. Use 250 words at least, be done in 500 words. So that has to be a fairly simple setup.
You need to also have your inciting incident: Put it at the 15% mark, 750 words (i.e. there are 750 words BEFORE the first sentence of the inciting incident).
The inciting incident will typically introduce the villain (or show a character already introduced to be the villain), sometimes remotely (by name, or on TV, or a story being told by somebody). The first act concludes at the 30% mark (1500 words for you) with a transition to Act II, this is when your MC leaves their familiar world (physically or metaphorically) and begins their journey.
I recently used Harry Potter and the Sorcerer's Stone as an example:
The inciting incident is at 15% (Harry's 11th birthday, Hagrid appears, and Harry's life will be changed by going to Hogwart's, Hagrid also tells Harry of Voldemort).
At 30% is the moment Harry boards the magic train to take him to Hogwart's, literally passing through a magic portal in the train station 9 3/4 to enter a new world. Within the next 5%, he meets both Ron and Hermione. Ron is an instant friend and sidekick for the rest of the novel (a good foil); Hermione is written more as a love interest; she is confident and smart and irritates the two boys at every turn (although Rowling chooses in the end to pair her with Ron, not Harry).
At 50% you introduce the first main turning point or discovery; for Harry that is discovering the Cerberus by accident, he and Ron are out after curfew and trying to not get caught by Filch.
In the second half; you progress to the 90% mark (4500 words for you), to make the final discovery, and set up the final confrontation. For Harry, this is the confrontation with Quirrel at 93% to about 97%, followed by the wrap-up, victory is done, all is well, and back to the Normal World (until next year).
I suggest you take a novel you have read (preferably recently) and liked, and page through it for these key points, as percentage points in the novel, as I have done here. Use that as a model for your short story, whatever it is, identify these points and give yourself a word allowance for each. You can do as I did in less than an hour, find the structure.
Then write from the beginning with your word allowances. You don't start with 5000 words, you start with 250 words for your establishing scene (introduce your MC and the world): One page, for the layout I use in Word.
You won't have to kill your darlings, because you won't write any that won't fit. You know you can't spend a quarter of your allowance describing a teapot that has nothing to do with the plot. You have to pick the most important details that do the job, and focus on them.
When you have that 250 or 500, move on to the next, staying aware of the total so far. You need the inciting incident at 15%, 1500 words. If you spent 1000 words on the establishing shot, you only have 500 left! If you can't do it in two pages (250 words each) then fix the establishing shot.
Work through the novel you like; steal enough of that structure to give yourself 'milestones' of 5% to 10% in total length (so between 10 and 20 of them: The Sorcerer's Stone has 17 chapters).
Match your short story to that structure, and write each, staying within your limit. Remember 5000 is the max, so your limit is THE MAX, so finish each scene (chapter) with 10% to spare, so you have a little room to polish or backfill later (by backfill I mean add something to an earlier chapter to justify an event, skill, suspicion, or bias you discover you want in a later chapter, or to foreshadow an event in a later chapter). An easy way to do this is to calculate your percentages against 4500 words instead of 5000, giving you 500 words (about two pages) worth of backfill and revision.
Think of it as a clock on a long timed walk: If I am to be done in 4500 ticks, you need to be at point A by 5% (225 wd), point B by 15% (675 wd), point C by 30% (1350 wd). If you are too slow getting to point A, rewrite to make it faster or pick up the pace. Try to get to point B on time; do not let yourself get behind on three in a row. As you write, keep in mind the story must progress within one page (or two at the most) to the next station. Tangents that go too long become quite apparent, so you won't fill half a page with irrelevant poetry, and should never GET to the point of having a darling to kill.
Each Page will have a job to do and is your immediate puzzle to solve, and it will be far easier to get this one page right, than it would be to just start writing, end up with 30 pages, and then figure out how to cut 33% of it.