In general, in my experience, it seems to be based much more on need than want. Can your problem be solved without getting it? You might put it up for consideration here. Which means providing pictures of the situation including surroundings, and a good explanation of the problem, and why things need to be this way or that.

3 feet from the house? I would say this is a case of 'be careful what you wish for' in the making. Three feet is very, very tight. Imagine coming out of the house and walking almost instantly into your pool. Are you doing this to avoid moving a tree or other obstruction? Can we see what the area looks like (post pics)?

As an experiment, try putting an object like a hose or board of something else at the three foot mark where you intend your pool to be placed and go in and out of the doorway to see how comfortable or uncomfortable it would be to use the door to the pool area. I am pretty sure that it would be a selling objection (I'm a Realtor) should you ever sell your home - especially if the buyer had children. It would most definitely be a safety hazard. I would rethink this idea entirely.

Where I live you also need a fence around the pool. Maybe look at doing a lap pool instead of a regular one but 3’ is not wide enough for a walkway next to the house at all.

25 years spent in The Valley. No snark intended. Homes with pools are common, find one and buy it. Pools give no return on investment in your area.

You have to be careful on how close you come the house. You don't want to compromise the integrity of the house's foundation or structure.

Some variances can take months for a decision which may not be favorable to you

You're not getting a variance for that, I'll bet.

Ask you local zoning official for past precedence and provide an opinion on your case. Bring drawings of the lot with the house and pool correctly drawn to scale showing the 2' variance that you seek. I agree with above posters - the 2' difference is negligible. Stay with the 5' setback.