The first mentioned ( /infogixassure/entityresultlistdeletefiltered.sp ) is invoked when a user clicks "delete filtered" within the control data results popup window. If a query was opened with the listed results numbering in the millions, for example, 5 to 6 minutes is expected. For further information, the team may navigate to the "system" / "audit history" and search for "control data change" to determine if this may be the case. This will display what the user was doing, against what entity, filter criteria, etc.. This may be a valuable tool to verify what options may be available to improve the performance.
The second mentioned appears to be about ER, in particular the processing of "event queue" messages. There are "data purge" type events that are subscribed by various components, which may takes minutes to complete. Assure has similar event driven subscription processing for retention, and it is plausible that this may take minutes to complete there as well. Logs should provide more insight on this, which support would be happy to assist with, as needed.