I think you'll find the majority of homes in the Las Vegas valley are in a subdivision, the difference being if they have a homeowners association, or not. If you draw a rectangle from Sahara to Sunset north and south, and from Sandhill to Rainbow east and west, there are currently 38 homes that match your 3-5 bedrooms, 3 bath, with a pool. 34 of those are in areas without an HOA. If you extend that area out to the east and west it goes up to 81 homes and 61 without HOAs. I'd believe that if you expended that area possibly to the south you'd find some more that meet your needs.
These homes will range from foreclosures, short sales, and resales. Of course their condition can vary widely, the same for local amenities as well as what else you'd find desirable in an area.
If you'd like, I can set you up on a search that matches your specifics and cover a lot more details than you've listed here, typically more than you can find in the online searches. The results are sent to your email, and updated as soon as new listings are entered.
If you'd rather search for yourself for now, feel free to use any of my websites. I have 3 different ones so that you can chose which one you'll find easiest to use, and they don't require registration. Use the link below or you can access them all by clicking on my profile.
I hope that helps, and if you have any other questions feel free to ask.