Image size relative to Picture size when printing

You can set up your own Cropping presets or use the ones that come with Photoshop (see screenshot below).

Obviously if your desired aspect ratio for your prints is different from the camera's you must crop the image a little, that isn't normally a problem.

Make sure you have a minimum of 200PPI in your final image.

Hi, a camera has often a 2x3 ratio, some have a 16x9 ratio if you take a picture while shooting video.

without adding or substracting pixels, you can't fit a 2x3 ratio image on a 5x7 or 8x10 paper. It is akin to try to fit a square peg in a round hole...

You can substract pixels by cropping.

You could add pixels using Content-Aware Scale: 

https://www.youtube.com/watch?v=RlPsiJDMqkE

I'm not sure I understand the question. If the aspect ratio of your image does not match the aspect ratio of the paper, then you cannot print the image borderless and without cutting off anything, unless you would distort it. And 7x5, 6x8 and 8x10 are three different aspect ratios.