Sampling and Experiments · Superchallenge problem

In a matched-pairs experiment, one member of each of 5 pairs is chosen by coin flip to get a new diet and the other gets the old one. The weight losses (new minus old, in kg) for the 5 pairs are $3, 5, -1, 4, 6$. If the diet had no effect, each difference would be equally likely to have either sign (the coin flip decides which twin's result is subtracted). Under that assumption, what is the probability that the sum of the 5 differences is at least as large as the one observed?