I take it to mean 'aura lieu' as per this definition from the oxforddictionnaires.com SET: Give someone (a task or test) to do:schools will begin to set mock tests.
I think it would say "we will set for the 5th.." is they meant "ils vont decider d'une date"
I understand your uncertainty, SteAgate. As written, the sentence could mean that the test will take place on 5 Jan, or that the examiners will prepare the test (set the questions) on 5 Jan, or that the decision on the date will be taken on 5 Jan. However, the context suggests that the first meaning ('aura lieu') is most probably the intended one, because an invitation to a candidate is unlikely to include either of the other pieces of information.
It seems to me to be a badly written sentence. "We'd love to invite you to do the design test on the 5th of January" would be much clearer.