Should the total of my state and local income tax on my W-2 equal my taxes paid on the itemized deduction Schedule A? Should box 17 + 19 on W2 = box 5a on Schedule A?

[IreneS]

Most of the time. 

But the figure could also include other state/local taxes you paid in 2018.  For example if you owed on your state and local tax return for 2017, you would have paid the additional taxes in 2018.

You might also have withholding on a 1099-R.