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This is sort of like asking should you learn Swift or Objective-C, albeit much less difference between syntaxes. You can certainly get the job done on ES6, and the future is certainly in that direction, but all browsers still run ES5, so if you want to get paid for your work, you'd need to still know that syntax.

Babel is a great tool to let you use some of ES6's features now, but it will still help in debugging to know ES5 syntax since Babel transforms it at runtime.

If you been doing a lot of JS for web stuff, and used SO etc to check things but don't have a thorough understanding of the language I would recommend the book "JavaScript the good parts"

JavaScript the Good Parts shouldn't be the recommended book anymore (and I think even Crockford himself said something along that line in one of his newer videos, couldn't find it though... it's been a while)

Why not? I found it more useful than Eloquent Javascript at least

Just learn ES5 and then take the 10 minutes it takes to learn ES6's features. It doesn't add that much.