My Panasonic Lumix DMC-ZS15 P&S (about 2yrs. old, records in JPEG) takes fine pictures for my purposes (at most 5x7 prints). It has 12.1MP, 16x zoom, and a 1/2.3 MOS sensor. I always use the "high quality" setting and auto settings for aperture and shutter. I have always wondered which MP setting would give me the best resolution vs. noise in the final image. I asked a similar question 2days ago, but now I am looking for a more specific answer. I realize this new question may be more specific, elementary,and possibly neurotic than you guys care to deal with, so please feel free to ignore me if that is the case. I have experimented and learned that I probably do not need all 12MP but still cannot make up my mind between 5 & 8MP. Thank you for your consideration.
12.1 MP is still the best bet if you'll be printing. You can always apply your own down-scaling after the fact, but you can't go the other way. At worst, you might lose a minute amount of noise reduction from down-scaling from a JPEG rather than from the sensor itself, however having more data points to work from and downscaling to the native resolution of the printer (or a multiple there of) will give you a higher overall quality than what you might lose from the downscaling from a JPEG.
If you are going to be going to screen only, then there might be a slight advantage to using a smaller size, but the primary advantage is still the fact it takes up less space on the card.
Let's use math!
5 megapixels is 5 million pixels. Divide by 5, divide by 7, and take the square root and you get
377.96 dots per inch. This is within the realm of decent print quality, but just barely. It's not very impressive. 8 megapixels will get you ~478 dots per inch. This is better. 12 megapixels will get you 585dpi, better still. Even a cheap home photo printer will easily be capable of printing at 600dpi, so you're not throwing away pixels.
You'll also lose some image quality by shooting in JPEG. You'll lose a little more if you shoot in JPEG and then do photomanipulations like color adjustments (and you'll lose pixels directly if you crop). I'd say you probably want all 12 megapixels if you can manage it.
Noise reduction is unlikely to be worth the lost pixels. If you want to reduce noise, shoot with good light, wide apertures, and/or slow shutter speeds. (These things are not without tradeoffs, naturally).