Most appropriate statistical treatment where participants select five statements from a list I generated a list of 35 proven benefits on a subject and asked the public to choose five which would be most likely to influence their behaviour.
43 respondents cast 215 votes, and three of the benefits received many more votes than the others.
What would be the best statistical tool to measure the significance of this result?
Clarifications: The research has been motivated by the practical difficulty of promoting all 35 benefits to the public, in order to generate a change in behaviour.  The research aim was to make an initial determination whether each benefit was likely to have an equal influence on the public. Before seeing the responses I expected a fairly even distribution across all benefits but this was not the case. The top three benefits were at least 10 votes clear of the fourth most popular. Four benefits received no votes at all.  I hope to demonstrate the pattern of response is statistically significant for x number of the benefits, and that future promotional material should focus on these as the most likely benefits to generate change.
Each of the benefits is distinct from the other, though the first 13 would come under the category of environmental, then 9 economic and 13 social, and it would be desirable to consider the data by these groups in addition to considering each individual benefit.
The respondents selected the five benefits from the list of 35 that were most likely to influence a change in their behaviour, they did not rank their five choices and successive votes did not affect previous ones, other than you could only vote for each benefit once.
Many thanks for the initial responses and prompts to clarify and I hope I have remembered everything!
 A: One clarifying question: are you interested in the significance of the three top responses jointly, or each of them individually?  This probably wouldn't affect which general method you choose, but would affect the test statistic.
Second clarification: how related are the responses?  (I mention this below, too.)  For instance, it could be the case that potential responses 1-5 are essentially identical ("lower price" and "costs less"), as an extreme example, and that 6-10, 11-15, etc., are also, in which case the data would really be 43 single votes for one of 7 options; or all 35 are completely different ("lower price", "dogs are loyal companions"); or different sized groupings of similar but not identical responses.
The first idea that came to mind for me was permutation tests.  [Ultimately, I'm not sure this is a good idea, but I will leave what I originally wrote.]  Philip Good's text is a good start; this link has the entire book in PDF format.  The key assumption is "exchangeability" under the null hypothesis; see Section 2.2.2, page 24, and Appendix A.5, where he defines, "the joint distribution of the observations is invariant under
permutations of the subscripts" (Good p. 268); more of my thoughts below.  If that assumption is satisfied, permutation tests are exact, unbiased, nonparametric tests.  The only other difficulty I can think of is computation.  35! is approximately 10 duodecillion...too big to compute every single permutation (again, unless there is some valid way to group responses?).  Chapter 14 in the book, "Increasing Computational Efficiency," discusses seven techniques (it says); of course, the "exactness" would be lost, but might still be a good option.  I think the more critical piece is exchangeability.
Re: exchangeability, I think for you it would depend on how related the responses are to each other.  For your setup, it would be the indices of the 35 potential responses that you would want "exchangeable."  If there are clumps that are very similar, maybe you could group them somehow...?  Even if everyone had only voted once, and you can assume the people are independently sampled, if response options have some dependence structure, the results wouldn't be exchangeable.  It only gets trickier if the distribution of my second vote depends on my first vote, but doesn't depend on the previous person's first vote.
So the second idea would be some sort of bootstrap.  You could resample at the unit of the person (43 in your sample), which I think would take care of the intra-person vote dependence.  Your test statistic would either combine the three categories you mentioned, or treat one at a time.  Perhaps a way to get a pivotal statistic, but I can't think of one right now.
Other than that, I'm not sure.  If you assumed any one of the 35 were distributed binomial(215,1/35), I don't think that would quite be right given the dependence issues.  So I'm curious what others will suggest for you, and the best I can suggest meanwhile is a bootstrap at the person level.
Dave
A: Since you were asking your respondents to make a choice, you would want to look at literature on choice modeling. This has been developed in econometrics to a far greater extent than in any other discipline (and, interestingly, in transportation research, which has, to a great extent, been relying on econometricians pushing the methodology). I believe you have a weird twist on a multinomial logistic model or a conditional logistic model. If you find an appropriate extension (five selected alternatives rather than one, as in the standard multinomial logit), and you fit an intercepts only model, it will tell you by how much some alternatives are more likely to be chosen than others. The framework will also allow you to have covariates, so you would also be able to dissect how the demographics of your respondents affects the choices they make.
