Yes you can solve things faster than they can, that's why you are senior and they are not. However, a good senior wants to take his juniors to the senior level as well and the only way you can do this is by letting them learn how to do things.
Mentoring is the most effective use of your time right now, not coding.
Look at it this way, if you spend the next six months mentoring effectively and the juniors learn enough to become intermediate developers - then you have 5 intermnediate develoeprs and one senior. If you do all the hard work yourself because it is faster, in six months you wil stil lhave 5 juniors twiddling their thumbs (well the best of them will have moved on to other jobs by then if you give them no challenging work, so you may have fewer or newer junior devlopers) and one overworked and cranky senior.
You know what complex interactions are typically found in the bugs, so develop some training specifically on those types if things, how to troublshoot and find the actual problem and then the types of methods typically needed to fix them. Then give them those problems as they come up. Yes they will take longer to fix them and you should allow for that in your time estimates.
The pair programming idea is great. Pair with a different one for each problem that is truly advanced. Even if they don't know enough to solve the problem yet, having the junior at the keyboard while you tell them what to try in terms of looking for the cause will help teach them the process of troubleshooting. Of course, don't just expect them to take dictaion. explain what you want them to look for and why. Ask for their ideas and listen to them. Explain why their idea is not a good choice if it is not. Use the Socratic method of teaching by asking leading questions. They will remember better the solution they came up with themselves through your leading questions than the one you dictated to them without explanation. They will aslo remember better if they actaully typed the solution rather than just watched you type it. One of the main priciples of learning is that people retain more if they do rather than just listen.
Once the junior has helped you solve a particular class of problems as part of a pair with you, you can pair him up with someone else the next time that class of problem comes up and only be available for consulting, not standing over their shoulders while they try different things.
You have five new people which is really hard. You need to be fair to all of them and rotate who you pair with or give the guidance to. Don't play favorites. BUt you wil also need to be a person who provides "Tough love" if someone is not succeeding and making progress. YOu may need to call one or more of them aside and tell them that they need to improve and why you feel they are not succeeding. SOme peopel will let you do all teh work if you pair and you can;t allow this just becasue it is easier. If teh person can't do the work, it is kinder to them and much better for your team if you don't carry them once it is obvious that they cannot or will not learn to be more independent.
Remember, you get what you expect. If you don't expect much, you won't get much. Expect them to shine and most of them will come up to your standard.