Can relative timestamp be used for reporting on a 15, 10, or 5 minute scale instead of days

The relative dates (or relative timestamps) do not allow specifying a time frame less than a day at the moment. What you can try instead is create a parameter with an expression like this: 

new Date(System.currentTimeMillis()-15*60*1000) 

and then use this parameter in report query. This expression will return a timestamp for current time minus 15 minutes (where 15 is minutes, 60 is seconds and 1000 is milliseconds). You can also create a separate parameter for the number of minutes and use it in the expression, e.g.: 

new Date(System.currentTimeMillis()-$P{minutes}*60*1000) 

Then you can create an input control for $P{minutes} and users will be able to specify the number of minutes. Also in this case make sure that the $P{minutes} parameter is defined first, and the parameter with the expression above is defined afterwards., because the parameters are initialized by JasperReports engine in the same order they are defined.