I contributed 5,500 to a Traditional IRA account in 2017 then converted it at the beginning of 2018 to a Roth IRA. Is that something I'll claim during 2018 taxes?

Yes.

If the conversion happened in 2018, you will report that in 2019 when you file your 2018 tax return. 

But you still count the contribution on your 2017 tax return.

Be aware - The tax reform bill has removed the ability to recharacterize any Roth IRA conversions done in 2018 and onward.

I have the same question but these two answers seem contradictory. Is the Roth contribution counted for 2017 or 2018? TurboTax says "Answer Yes if you contribute by April 2018" but (maybe since I don't have a 1099-R yet for 2018?) it is also telling me that I have a penalty for contributions to the Roth (it's not recording it as a conversion).