I would say that your answer is actually correct and the book is wrong in this case, and let me tell you why. It seems likely that this is a very modern book and that if they would say it is a #11, they wouldn't penalize you for writing the technical correct b5.
Chords are based on scales. In a typical 7 note scale scale, you will write the intervals as so:
1 2 3 4 5 6 7
By this, I mean that every interval is accounted for: the first, the second, and so on. Remember that the 2 is also the 9, the 4 is also the 11, and the 6 is also the 13. But I'm keeping them as 2, 4, and 6 for my example.
Take this example of a myxolydian scale:
1 2 3 4 5 6 b7
You write it like this because every note in the scale is accounted for. This is technically the same:
1 2 3 4 5 6 #6
This is incorrect because technically we are missing the seventh scale degree.
So let's think of your chord as an example. A typical G Myxolydian scale is: G A B C D E F G which always corresponds to 1 2 3 4 5 6 (b)7. The notes you have in the chord are G F B Db Eb and Ab (In scalar order, G Ab B Db Eb F) The G corresponds to the 1st degree, the Ab to the b2 (or b9), the B to the 3, the Db to the b5, the Eb to the b6 (or b13) and the F to the b7.
No matter if the D is Db, D, D#, D##, Dbb, it will always be the 5th degree in the scale: so augmented, diminished, etc. If they had written C#, it WOULD have been a #11, but since we a) are using a D when referring to a G-rooted chord and b) do NOT also have a natural (perfect) 5 in the chord, we can conclude that it is actually a b5 and not a #11.
The fact that your book wrote G7 (b9, #11, b13) even though we don't have a natural 5, is confusing. Musicians would treat this as if there would be a D natural and a Db (C#). They should include that the chord omits the D (omit 5) or write the chord as you did.