Even when you purchase brand and shiny new jars in a box covered in plastic wrap, those jars are still not in a sterile environment. In addition to contamination by microorganisms that cannot be seen with our bare eyes, packaged jars may accumulate dust, small bits of debris, and even chips of glass in the case of breakage (which does happen sometimes in all the steps of transport from factory to store to home).
Whether brand new or re-used many times over, you should always clean jars just prior to filling them when canning. Wash jars in a dishwasher or by hand, using detergent and rinsing well. Clean jars should then be kept warm prior to filling. You can leave them in the closed dishwasher after the cycle, place them in your canner as it is preheating, or create a separate water bath to keep jars clean and warm.
Washing is also a good time to inspect jars for any cracks or chips, discarding or re-purposing those jars for non-canning uses if any imperfections are found. If you see scales or film from hard water left on your jars, then remove this by soaking jars for several hours in a solution containing 1 cup of vinegar (5% acidity) per gallon of water.
In order to actually sterilize jars, they need to be covered by boiling water for 10 minutes (at sea level…see note about altitude adjustment, below). When a process time is 10 minutes or more, the jars will be sterilized DURING processing in the canner. Therefore, when process times are 10 minutes or more, pre-sterilization of jars is not needed. It doesn’t hurt your product to do it anyway, but it does require additional time and energy and is unnecessary.
To pre-sterilize jars, place the cleaned jars right-side-up on a rack in a canner and fill the jars and canner with water to 1-inch above the tops of the jars. Bring the water to a boil and then boil for 10 minutes at altitudes less than 1,000 feet elevation. Add 1 additional minute for each additional 1,000 feet of elevation. When you are ready to fill the jars, remove the jars one at a time, emptying the water from them back into the canner. This will keep the hot water in the canner for processing filled jars.
Sometimes people choose to increase a 5-minute process time for certain jams and jellies to 10 minutes so that they do not have to pre-sterilize the jars. The extra process time is not harmful to most gels and spoilage should not be an issue as long as the filled jars get a full 10-minute treatment in boiling water. (And remember your altitude to increase this process time as needed.)
So, in summary:
Is a 5-minute process time enough to sterilize jars? No. If you are using a process time of only 5 minutes, such as for some jellied products, then you need to pre-sterilize jars before filling them (or increase the process time to 10 minutes, plus any altitude adjustments).
If a process time is 10 minutes or more (at sea level) then will the jars be sterilized? Yes, but be sure to wash and rinse them well, and keep warm, before filling them with food.