First, I learned it helps not treat this like a story line. Instead, treat it like a staircase. One thing at a time.
"Tp rollover 100k from retirement plan 403c"
Did you really mean 403(c)? That's not a retirement plan account; that's an Annuity, isn't it? Perhaps you meant 403(b).
"half to traiditonal IRA and half to ROTH"
The IRS has tables for what type of account is qualified to rollover to what other types, time frame minimums, taxable events, and between various types of accounts.
"Now tp have traditional IRA 50k.(from rollover) . 50K from traditional IRA is nontaxable"
Let's restate it for what happened: Transfer into Traditional isn't a taxable event. You should still know if the money that was transferred in came from a post-tax (basis) or pre-tax amount or some of each.
"and 50k from new roth IRA is taxable ."
The amount that went into the Roth would be a conversion, if it came out of an account that has only pre-tax contributions and earnings. Or, compute pro rata against basis.
If you confirm what happened is from a tax deferred account with only pre-tax contributions, then the Rollover amount that was converted by putting it into a Roth is the taxable event. Now it will grow tax free.
But, for instance, a Roth 401(k) or Roth 403(b) to a Roth IRA, means it was already post-tax, so that is more like a "traded straight across" event, and not a conversion.
"He opened new traditional IRA and contribute $5000 himself and $5000 his spouse"
That means a separate account for the spouse. Each account has one owner.
": non contribution deduction . They hav high income and AGI high"
Okay, so No Tax Benefit for contributing these funds. That makes them Basis = post-tax, or treated as already taxed before going into the accounts.
"He converts (backdoor roth from new account of traditional IRA ) $5000 to his roth IRA and his spouse $5000 from new traditional IRA convert to his spouse roth IRA"
But we also see there is another $50k in Traditional, so if that is an account that has earnings and/or deducted contributions and/or employer contributed funds (anything either never taxes, not yet taxes, or put in pre-tax), it is considered part of the computation.
There also is a provision to split "rollover conversion" per the IRS:
"Can I roll over my after-tax contributions to a Roth IRA and the earnings on my after-tax contributions to a traditional IRA?
Yes. Earnings associated with after-tax contributions are pretax amounts in your account. Thus, after-tax contributions can be rolled over to a Roth IRA without also including earnings. Under Notice 2014-54, you may roll over pretax amounts in a distribution to a traditional IRA and, in that case, the amounts will not be included in income until distributed from the IRA."
For example: A Roth 401(k) from my employer allows me to put in post-tax; but the employer match is pre-tax and goes into the 401(k) (not Roth), and perhaps they allow me to also put into the 401(k) once I exceed some limit on the Roth 401(k). That means I have Roth 401(k) that rolls to Roth IRA (straight across trade), some amount in 401(k) that goes to Trad IRA (never taxes and pre-tax) and some amount in the 401(k) (my post-tax basis amount) qualifies to go to the Roth IRA and all earnings go to the Trad IRA, because I just left that job.
"On tp: 5000+50000=55000. His tax free of $5000 conversion is (5000/55000)*5000=$454 and taxable 4545
On spouse 5000 is tax free because spouse has no traditional IRA
Am I correct?"
On spouse, yes. The taxpayer's situation depends on the source or origin of that $100k. You forgot about that Total. That's why I describe it as a staircase.
Let's assume everything falls into the "correct" category, no other basis, etc.
$100k from tax sheltered (deferred) and the transfer split the destination accounts, so All is distributed and half is Converted to Roth. That makes it half Taxable.
Then, he put $5k into Trad, making this $55k in Trad, and converts this $5k amount, so 9% taxable.
And don't forget: from now on until complete distribution, there is the Remaining component to track.
First year:
I put $50 nondeductible into the tax deferred account, and let's pretend the earnings double it. for the next year, I have $100 in Trad, half is my basis. I convert $80 (50/100 = half is Basis), so $40 is taxed on conversion (the "never taxed" share) and $40 is from basis. Now that entire $80 will grow in Roth tax free.
Meanwhile, $20 in Trad remains. Half ($10) still is my basis. That carries forward.
Now, the next year, it grows to $60. I decide to convert $50. That is 10/60 = about 16% basis, so about 84% taxable. That makes sense, because a majority is new earnings. So, $42 taxable and $8 is my basis and not taxable.
Now the account has $10 in it and $2 is my basis, so 20%.
Every year an account (or set of similar accounts owned by the same person) with Basis is still around, the basis is recomputed because of the prior activity that was pro rata.
It's a lot to review over text-based discussion. You might want to study investment materials to learn more.
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