I plan to visit Beijing from 19th May to 23rd May. Would I clash with any school public holidays ?

Vincent, there is no holiday during that time. You can do it. The nearest section should be Juyongguan, which is 35mi (56km) away. But I personally suggest you to Badaling. It is the most popular Great Wall section and can be easily accessed. You can take train S2 at Beijing North Railway Station directly to the wall. Hope you enjoy your trip!