5mtr is 16.4ft taking away about 2ft for the width of the projector gives 14.4ft. If the projector has rear air cooling vents rather than forward or side vents you will need to take in to account giving it more room to breath. Projector fan noise may also dictate placement, as you do not generally want to be sat directly below it.
Image size depends on the projectors throw ratio, distance from screen to width of image projected. It varies from projector model to projector model. A typical short throw projector is 1.55-1.7 throw ratio, it is given as a range because they have zoom lenses so you can alter the size of the image slightly without moving the projector. 14.4/1.55 = 9.3ft. Projector image size is measure by width not diagonal so that gives you 5.2ft high and 9.3ft wide image, about 128 inch diagonal.
You genrally want viewer distance to be about 1.5x screen width (not diagonal). Some people prefer as close as 1x screen width others upto 2x screen width or further.
Since you can project the same image size from different distances by using the lens zoom, the question of what is best projector closest to the screen or projector farthest from the screen arises. The zoom effects brightness and to a lesser extent contrast. To calculate the effect on brightness you use the lens f numbers. (f1/f2)squared. For example a projector listed as having a f2.6-2.4 lens works out as (f2.4 largest image / f2.6 smallest image) squared = 85.2. 100 - 85.2 = 14.8% loss of light, largest image 100%,smallest image 85.2%. The effect on contrast is the opposite way round it is higher in the smallest image, and is typically alot less than the difference in light output, about 7% or less. Depending on lens quality the smallest image will also usually be sharper than the largest image, but with some projectors the middle of the focus range may give the sharpest image. Since contrast has a bigger effect on perceived picture quality than brightness, as long as the image is bright enough, it is usually best to project the smallest image. To determine lens focus and sharpness you want an image of black lines on a white background and face inches from the screen look for the least chromatic abberation (the black does not go sharply into white, but has a colored edge) at the extremes of the screen, or with DLP projectors how sharp the individual pixel structure looks.
You also need to take into account the projector offset, the angle its lens aims at the center of the screen. DLP projectors normally have no adjustable up/down lens shift, while some LCD projectors do. Offset is given is a percentage of the screen height that the projector (center of lens) must be mounted from the furthest vertical point of the screen. For example a fixed offset of 136% percent with a screen 62.4" in height, means that this projector would need to be mounted 84.86" above the bottom of the screen for a ceiling mount. 136% * 62.4" = 1.36 * 62.4" = 84.86" Projectors also have digital keystone adjustment to compensate for incorrect placement but it is best avoided.
DLP projectors normally have no adjustable left/right lens shift, while LCD projectors usually do. So DLP projectors are ideally placed lining up with the center of the screen, to avoid having to using digital keystone adjustment. While LCD projector have some leeway to be placed to the right or left side of the centerline.
Image brightness wants to be around 12ftL but varies by personal preference, some people go as low as 8ftL in dedicated batcaves, some as high as 24ftL in rooms with some ambient lighting. The projectors quoted Lumance ratting devided by the surface area of the image in feet gives ftL. So with a 5.2ft x 9.3ft image you would devide Luminance by 48.36 to give ftL. Due to overly optomistic manufactures specifications you usually want to treat their Luminance values as half what they quote, the lamp will dim with age as well, and if too bright you can use a camera neutral densitiy filter. A matt white wall is taken to have a gain of x1, but you can use high gain or low gain screens. A overly bright DLP projector will induce DLP rainbow effect.
You can project on to a flat matt wall, no problem. For the best neutral white paint or paint mixes, I would search on google for home cinema enthusiast forums. Some people prefer screens especially in non-ideal viewing conditions. In ideal viewing conditions a while a matt white screen is usually the easiest option and will not perform much if any better than a white flat matt wall.
Any ambient lighting in the room will washout the image contrast. Even without any other sources of light, the projected image itself will reflect into the room, bounce of the walls, ceiling, floor and back onto the screen washing out some simultaneous contrast. Dedicated home cinemas are often black to get maximum picture quality. A greyscreen or one with directional gain will help offset non-ideal viewing conditions.
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