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So I'm pass the income threshold to contribute to a ROTH IRA, but I understand I can always contribute to an IRA up to the limits...
but my question is... since I can't deduct the contribution... doesn't it mean that I will be double taxed on the principle? It seems like when you take money from IRA after 65, everything is counted as income. So if I put in $5,000, when I take that money out, I have to pay taxes on that again? Am I being double taxed?
Yes, you can make a "non-deductible" Traditional IRA contribution. You must report non-deductible Traditional IRA contributions on Form 8606 part I for the year the contribution counts under.
The after-tax principal amount (the "basis") will not be taxed upon withdrawal; only the earnings (which are always pre-tax in Traditional IRA, even if it grew from after-tax funds) and deductible contributions will be taxed upon withdrawal. (Note that a withdrawal from Traditional IRA will generally consist of pre-tax and after-tax amounts in equal proportion to the pre-tax and after-tax amounts in the Traditional IRA overall, due to the pro-rata rule.) You will calculate the taxable part of a distribution from Traditional IRA in Form 8606 part I in the year you withdraw.
Assuming you did not have any previous money in pre-tax IRAs, one thing you can do is a "back-door Roth IRA contribution" -- after you make your non-deductible contribution, immediately convert the amount to Roth IRA (this also does not have income limits). The end result (again, assuming you did not have any previous money in pre-tax IRAs, so you don't have issues with the pro-rata rule) is the same as a regular Roth IRA contribution, which is better than a non-deductible Traditional IRA contribution because the earnings are after-tax too.
