So I read the bill, which was no fun, and did find the part you're talking about. The way the definition of "machinegun" is worded does indeed say

"

...and fired therefrom at the rate of five or more shots per second.

However that is not an independent sentence or statement. One of the requirements of being a Machine Gun listed prior to the five shots per second states this:

...or any other mechanism or instrument not requiring that the trigger be pressed for each shot...

So the way I'm reading it, the five shots per second is kind of irrelevant. The gun has to meet all the basic requirements of a machine gun before the 5 shots thing even gets considered.

If I were you I'd be more worried about some of the loose terminology in there like "mechanical rifle". What the heck is that?