I contributed $6000 of post-taxed funds (income saved in my bank account from my job) to my Roth IRA. I thought better of this and decided to withdraw $5000 and put in other investments, believing that only withdrawals based on earnings are taxable. Is this true?
If you have had your Roth IRA for at least five years or are over 59 1/2, you can take the withdrawal of your contributions with no penalty.
No, you will not be taxed on your distribution that comes only from contribution basis. If the distribution is not a qualified distribution (and from your question it seems that it is not), TurboTax will prepare Form 8606 Part III to calculate that the taxable amount of the distribution is zero. Be sure to enter the $6,000 Roth IRA contribution (if made in the same year) and after entering the Form 1099-R be sure to click the Continue button on the page the lists the Forms 1099-R that you've entered so that you can supply or confirm the additional information that TurboTax needs to be able to properly prepare Form 8606.
I'm not sure why you wouldn't have just made the same investment within a Roth IRA so that gains will eventually be tax-free, transferring the funds to a different Roth IRA if the one that you have now cannot hold the particular investment. (Of course there are also certain investments that are not permitted to be held in an IRA.)