If you're importing files in the XLS, XLSX or VCF formats, you can actually import upto 5000 records per batch. These could be the reasons why you cannot import more than 5000 records:
The import file is not in the CSV format - If you want to import more than 5000 records, the file should be in CSV format.
You are using the Free Edition - You can import only 1000 records in the Free Edition. In the Standard Edition, you can import 10,000 records per batch, 20,000 records oer batch using the Professional Edition and 30,000 records per batch using the Enterprise Edition.