Well, both are used with masculine nouns, the absolute form חֲמִשָּׁה, when it is undetermined (חֲמִשָּׁה גְּבָרִים five men), the construct form חֲמֵ֫שֶׁת, when it is determined (חֲמֵ֫שֶׁת הַגְּבָרִים the five men).
Non-native disclaimer in place: I think that is wrong. I think that five of the ducks would be: חמישה מהברווזים שותים מים. Or the number might be in the construct... but I am fairly sure it doesn't translate this sentence.
Interesting question. What do the ת and the ה add to this sentence? Note that the popup hint even offers that חמשת means "five of". So, I think you have a good point, and, if marked wrong, should report it. Then let's see what the moderators conclude.