The information is processed 'separately' at 5 'different' planes

It depends on the context, but it certainly doesn't need to be redundant in general.

Using different terminology (because what's in the question isn't entirely clear), contrast the following sentences:

1. The work is handled separately at 5 different office locations.

   • Five different and independent sets of work are conducted. The employees in the different office locations have no contact with each other, and they separately submit their work to a shared manager.

2. The work is handled jointly at 5 different office locations.

   • A single set of work is conducted. The employees in the different office locations collaborate on the work, and they jointly submit their combined work to a shared manager.

So:

"The work is handled at 5 different office locations."
"Oh, is the work handled separately or jointly?"

Although the terminology is different here, the general construction of the sentence and its meaning is likely the same.