OK Wayne,
1st question: What's the model number on the Light relay unit?
That being aside, I'd set up a phantom module with a timer during the daylight hours (let's say, for example, A1). Lets put the light module on address A2.
Set up a macro that activates on address A1 that sets flag 1 when the module turns on, and another that clears flag 1 when the module turns off. This takes care of establishing daylight hours.
Next, I'd set up a macro on address A3 which has a condition that Flag 1 is set. In this macro A2 fires for 5 seconds then shuts off. Then I'd set a delay for 5 minutes and fires address A3 again. Warning: looping macros can cause problems, and need to be purged to stop the process. Next assign a timer to the macro on A3 that starts this thing in the morning.
This should be a good start, but can't rule out that there might be a gremlin in the works.
I hope that others will chime in.