The Race Director

First you'll need to set up Tailor > Options > Results 1. Change the Race Segments dropdown to Two Segments then click the Timing Points button. Here you define how many physical timing points you will have. In your case it is just one. Set the Occur Ct to 2 so that RD will look for two passings per participant on this Timing Point, then set the Gap Factor to something less that the fastest time that you expect in a lap (maybe 12 minutes for a 5k loop). Then click OK.

Now check the Segment Definitions Vary By Division checkbox, as we will be defining Segment Definitions differently in the 5k than the 10k (The 5k will have one segment, and the 10k will have two).

Now you can close out of this screen and go to Tailor > Divisions.

Select the 5k division on the left, then click Segments and type in the Segment Count. For your case this should be 1. 

On the next screen you'll want it to look like this (the Report Heading can be anything you like): 

Next click Save and we'll do the same with the 10k, but defining 2 segments instead of 1.

In this case we'll need to set the Occurrence for the second segment to 2, so RD will count the second read at this Timing Point as the time to use for this Segment.

Then click Save and you are all set!

Let me know if you have any questions.