I have an old antique photo that I need to resize for printing from a printing shop, howerver, how do I resize a small 5x7 cm to a large , 20x20cm after being restored.I dont want to have the photos be compromised by the quality . thanks
How is the image being restored? If you're scanning a print, transparency or negative, then you're best getting the scan at larger than you think the print will be, and using that size to do any retouching required.
Depending on the original, things will look however they look. Just make sure you get the highest quality scan possible (highest quality in terms of scanning operator and scanner, not necessarily in terms of biggest file size).
If you need to scale up the image (you shouldn't), then do this as the first step, and scale to an exact multiple, if you can (200%, 300%, 400%), even if that means the final image is slightly higher than 300DPI for your purpose.
From there, retouch as required and output as a print when done. It's probably a good idea to keep the original scan file, just in case you realise you made a mistake with some of the retouching.
Hope that helps.
You probably realise this, but it's worth stating: if you need a rectangular 5x7 cm photo to fit a square 20x20cm final image, you're going to have to resize it proportionally to 20cm x 28cm, then crop the image down to a square, to prevent distortion.
(The exception would be if you use Photoshop's content-aware scaling, or other heavy retouching, but you'd still have to chnage the shape of your image).