The fatalities in the article I linked were from US National Parks, and the odds of death were calculated using those National Park fatality numbers against National Park visitor numbers.

To calculate odds of death using your 5 alligator fatalities in the US you would need to calculate those 5 deaths against the entire population of the US, which is a great deal larger than the number of National Park visitors.

Likewise for the 17 bear fatalities in "north American", to calculate odds of death you would need to calculate those 17 against the entire population of North America, including Canada and Mexico.

Bottom line is that a basic statistical calculation using your numbers will very likely show an even lower chance of death from bears or alligators than do the National Park statistics.