In Origin version five the best way to have a border around a graph is to turn on the top X and the Right Y axis, with no tick marks or labels. There is no provision for altering the frame thickness.First select from the Origin Menu bar:
Format: Axis: X axis
Select the Title and Format tab and check off Show Axis and Ticks for the top X axis.
Next change the Major and Minor Ticks to NONE.
Click on OK. You can set the thickness of the Axis to any thickness you want.
You will need to repeat this procedure for the Right Y axis.