Often, it will be enough to know that you have a 1,200bp insert in a 5,000bp backbone, but there are many plasmids out there that, when digested with restriction enzymes common to multiple cloning sites, will result in similar sized bands, thus making this simple digest less informative. This is particularly true if you receive a plasmid from someone in another lab, or dig one out of the freezer and you are not 100% sure it is what you are looking for, but you have a map and know exactly what it should be. A useful restriction enzyme based technique for verifying plasmids like this is "plasmid fingerprinting", where you cut the plasmid into 3-8 pieces such that all (or most) fragments are small enough to be accurately sized on a gel and also such that they are different enough in size to be easily resolved from each other. However, by choosing an enzyme or enzymes that will cut your plasmid into multiple fragments, you can get a very unique pattern that will distinguish one 5kb backbone with a 1.2kb insert from all others.
When choosing restriction enzymes for this approach, it is often a good idea to choose two different enzymes that will give you unique but distinct patterns so that you get double confirmation. In the example above, digestion with either RE3 or RE4 will give a very predictable pattern of bands on the gel, but by digesting with both and seeing both patterns you can be incredibly confident that you have the correct plasmid.