The way I see it, you would need a ginormous catastrophe to happen, of historical and global proportions. Any non-catastrophical measure (taxes, regulations, phase out of meat, education...) is going to require longer than 10 years, or is going to face resistance from part or the whole population.
So there are three factors of which you could only have two at the most:
- Short time frame
- No resistance
- No catastrophe
Short time frame + No resistance
This is what you want in your question: short time frame and without people resistance.. and for that to happen, you need a catastrophe that forces an immediate change: either cultural (people changing their mind from one day to another) or in resources (a plague that kills every animal but/including humans).
You would need to make sure that the catastrophe is natural and not man-made (e.g. war, killing of livestock, killing all meat eaters...), or it is going face resistance from sectors of the country's population (if not from all of it).
Also that catastrophe would have to be at a global level affecting all the countries in the world, or otherwise that country would probably be able to import meat from a neighboring country, stopping or slowing the process to more than the requested 5-10 years.
No resistance + No catastrophe
If you want no resistance by the population and no catastrophe, then you won't be able to reach it in such a short time frame. You need a deep change of culture in that country's society, and that doesn't happen in 5-10 years: it would take generations.
Willow said 50-75 years in this answer, I am going to risk and say it would be more than double (or even triple) that. You would need a full reset in the country's population to achieve it: and by that I mean until no-one alive in the country knew anyone alive when the cultural change started...
And probably even then, there wouldn't be a total cultural change. Imagine something as "simple" as accepting people regardless of their skin color. It has been over 150 years since the US Civil War, and there are still many Americans that suffer discrimination and hate based on the same beliefs that caused the war (I understand that this is an oversimplification).
Short time frame + No catastrophe
If you want short time frame and no catastrophe, you are going to find resistance:
- Old people will refuse to change their old habits;
- The general population will complain that taxes are too high;
- Farmers will complain of the new regulations (or cheat);
- Rich people will find ways to circumvent the change...
Again, you would need a deep cultural change, and that doesn't happen overnight or without a fight: big changes will bring big resistance in one way or another. It will be unavoidable.
And the way that you deal with the resistance will probably create more resistance. For example, if you punish the meat eaters in harsh ways, many people may change out of fear, but many people will also join the resistance.