Hi!
Thanks for your post and sorry for the trouble!
The reason for this basically is that this is a rather large table, with over 5000 rows. That amount of data has to be transferred from the server to the browser, and then the visitor features, like sorting, searching, etc. have to be initialized. This simply takes a few moments.
Now, there are possible solutions: Instead of loading all tables data at once, it might make sense to only load the relevant data at a time (like the first page of the table, or maybe only filter results), so that the amount of transferred data is much smaller, which will also speed up the processing of the visitor features. This is possible with the Advanced Loading and Server-side Processing feature modules, which are part of the TablePress Max premium license plan. So, if upgrading to that would be a possibility for you, these are the features that I would recommend for making this table load much faster.
Best wishes,
Tobias