Its 4 (D) . Jane is singular and needs the singular verb "is".

An additional thing that may help you is that an additive phrase does not change a singular noun/subject into a plural noun. Only the conjunction "and" can make a subject plural.

I picked 4 too, but I was wrong.

I guess its 5 then. The test makers probably consider choice 5 the most concise and least awkward, even though I don't understand why 4 is "awkward".

Yes the answer is 5(E). It can only be redundancy which invalidates 4(D).

I chose 4 as well and was clearly wrong. I don't understand why 5 would be correct. Removing the middle we would get "Jane is flying to Seoul on a business trip." Looks and Sounds correct to me... Can someone please explain?

has to be 4

5 cannot be answer here

That's why I always ask for sources. We dont want to skew any1's reasoning by doing such sub-standard quality SCs

anyways coming back to the SC question
for 5th
Jane, John and their three children are

THEIR is at issue, here.
THEIR does not have a clear referrent

I don't see any problem with noun referral with "their" in option E - it obviously refers to the only two nouns mentioned before "their", hence no ambiguity there...
However, I do think in option D their has a referral problem (John and their?) and is illogical if used with the singular "is" since it says their children!...If it were
Jane, accompanied by John and HIS children,IS flying......
this would be correct though obviously it would change the meaning of the sentence, I am only saying grammatically correct.
Answer is unequivocally E

E is the best choice because it is concise. Also E gives a clear meaning to the sentence by saying that "Jane, John and their children" all are travelling.