When you refer to 5R printing size, does it indicate the number of pixels left for the file ? Which application did you use to save file in 5R dimension ? Dimension is not equivalent to size of the image. You have to put in the density of the image to get the total number of pixels required.
Next is when you save the file, assuming JPEG, did you get to choose the quality you save ? JPEG can be either lossy or lossless compression depending on the settings used. The actual colours and tones arrangement of the photo will also contribute to different file sizes, but it be quite unlikely to drop from 7MB to 800KB without drastic change to the original image should the size retain. If the size is changed, then it is most likely the case.
Check the Image Size in Photoshop. It will give you the gauge on the maximum print size without compromising the quality. Ideally for print, the resolution should be at least 300 dpi (or pixel per inch). In Photoshop, there are Pixel Dimensions and Document Size. There is a correlation between the two and the Resolution.
Uncheck Resample Image and change the Resolution to 300. Check the Document Size. If it is at least 5 inches by 7 inches, then it is good for print. Otherwise, you can check Resample Image and select Bicubic Smoother. Set the Resolution to 300 and Change the Document Size to the desired dimensions. However, I cannot guarantee that the printout will be sharp.