more than 5000 records

You cannot query all 5000 records at once since it will lead to performance issues and the query will time out. You can try to query the data in batches of 10 or 20. And showing all 5000 records at once will not be looking good as well from UI point of view.

You can query the data once some value is entered in the custom picker which can be used as a filter.

I'm using pagination and showing 10 records per page , but in my data table having more than 5k records, how can I display or shown under search 5001th record ?

I'm using pagination and showing 10 records per page , but in my data table having more than 5k records, how can I display or shown under search 5001th record ?

On what basis will the 5001th record will be displayed?
If its based on the value entered on the custom picker, just pass it as filter to the query then it will work similar to what you have implemented. You dont need to worry about anything else. The pagination and other things will take care. Whatever is matching that picker value, will get displayed in the first 10 rows. If its more than 10, it will be in the next page which will get queried when you move to the next page.