Firstly, I think its 'so that' instead of 'show that', else the question wont have any meaning.Please check that out.If I am right, the solution is as follows:
As degree of polynomial to be added is less than that of q(x), let ax+b be added.
So the polynomial becomes 5x4+6x3-13x2+ (a-44)x+(7+b).
On dividing it we get the quotient as 5x2-14x+28, and remainder as (a-114)x + (b-77)
As the polynomial p(x) is completely divisible by q(x), so the remainder should be zero.
Hence, (a-114)x + (b-77) = 0
=> a=114 & b = 77
So 114x + 77 should be added to p(x) so that to be completely divisible by q(x)
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