P = Protection Class
5 = Accuracy Number in percentage. It means the maximum permissible error will be 5%
20 = Accuracy limit factor indicates that the CT will sense the current with the specified accuracy even with 20 times of its secondary current flows in the secondary.
This is required for protection Core of CT, because the fault current is high and the CT should be able to sense the high fault current accurately to protect the system. Further, when there is fault, the accuracy is not that important. A fault current of 20 KA or 21 KA may not matter much. What is important is the CT should not saturate so that the protection acts.
For example, if the CT is 1000/1 , then in case of fault, when the fault current is 20000A, then the secondary current is 20 A +/- 5%.
Similarly 5P10 can be explained as CT will sense the current with the specified accuracy of 5% even with 10 times of its secondary current flows in the secondary. For example, if the CT is 1000/1 , then in case of fault, when the fault current is 10000A, then the secondary current is 10 A +/- 5%.