A plan is when you have outlined the exact steps to take, envisioned alternate scenarios and have worked out how you will act or react under the different possible circumstances. A plan is a guideline, a workbook, a manual that you can stick to blindly. A plan is something that you execute on.
This being the case, it puts constraints on how long you can plan for. If you work in sprints, you plan for either one week or two at the most. For most things I do, I personally plan for no longer than a week. Every Sunday night is when I sit down to plan for the week ahead. And only for the week ahead.
A three month plan is pushing the limits. And a one year plan or a five year plan is just embracing stupidity. There is no point in planning that far ahead, because new things will be revealed to us in the time between now and then which will change how we want to go about things.
However, a commitment works the opposite way.
A commitment to be financially more responsible, to lead a healthier lifestyle, to solve a hard problem (the kind that result in PhD theses and publications) is long term.
It doesn't make any sense to be committed to one of these things for a day or a week or a month and then to re-evaluate at the end of that time frame.
In order to make a difference, the commitment needs to be for longer.
When you're committed, there is no semblance of a plan. There is just an end state that you have in mind and you are dedicating your time and energy over the committed period to achieving that.
If you have a five year plan, throw it out of the window. What you need is a five year commitment.