Going back to a previous employer can definitely be possible. But obviously it depends on how you left the previous employer. I haven't done so myself, but I have a few experiences telling me that it is possible.
What to tell them
Explaining that your new job doesn't live up to your expectations was definitely a sensible thing to do. That is the single most likely reason to want to come back.
This might not be sufficient for them. They may fear that you are going to leave again soon when another offer comes up. If you have given the impression that you were unhappy with your previous job, it is a quite natural concern for them to have.
There are however a few points speaking against that. If you were unhappy with your previous job from the first month you worked there, you wouldn't have stayed for five years. Moreover wanting to come back after having been somewhere else sends a clear signal that you were not really unhappy with your previous job and that you might even be less likely to leave again given your current unsatisfying experience.
It is also possible that they might actually have been happy to see you leave in the first place. In some jurisdictions it can quite difficult to get rid of an employee once the company has hired them. If an employee only gets stay because they are difficult to get rid of, then that employee won't be coming back after having resigned. I have no way of knowing whether this would apply to you.
Knowledge of what was said by you and your previous employer when you resigned could give a better understanding of why they might be hesitating to take you back.
My own experience
Several years ago I was interviewing for a job. One of the companies where I had applied turned me down because a previous employer of said company wanted to come back and they were going to give the position to him rather than to me.
At a later time I resigned from a job after having worked at that company for four months. I explained my reasons for leaving which was that I had received an offer which was better suited for my qualifications and gave a 50% higher salary. Upon me leaving they made it clear to me that in case my new job did not live up to my expectations they would be interested in me coming back.
I resigned from another job after 4½ years. In this case I explained that it had been a very difficult decision for me because I had been very happy with my job at that company. My manager at that company explained to me that if I should change my mind they would very much like to see me back and made sure to mention a company policy about a shorter interview process for anybody coming back within the first half year.
It has been 4 years since I left that company and lately they have been contacting me every 6 months to hear if I might be interested in coming back.