Pass a parameter ($dropdownvalue) to the method and use it with paginate:
public function getreport($dropdownvalue = 10) {
->Paginate($dropdownvalue);
For this to work, you also have to edit the route (route/web.php) so that it takes the value (what does your route look like?):
Route::get('/getreport/{dropdownvalue}', ['as'=>'report.get', 'uses' => 'ReportController@getreport']);
In order to show 5 reports at a time, you can access:
mydomaine.com/getreport/5
To use it with your dropdown, you need to "reload"/"redirect" the page after each selection. Simplest way would be to use javascript. Click here to see how.
Note that this is not the best way to do this but it works.