According to the Iowa-Illinois reciprocal agreement, I should only have to pay Iowa tax, even though I did work in Illinois. Were is Illinois form IL-W-5-NR?

you don't. as to your wife's income you only pay taxes on it in Iowa. there is no IL-W-5-NR in the Illinois state return. that is a form you either get online - see link -  or her employer. 

https://www2.illinois.gov/rev/forms/withholding/Documents/currentyear/il-w-5-nr.pdf 

 

if Illinois taxes were withheld you'll have to file in Illinois to get them back.

you need to file form IL-1040 and schedule NR which is not yet available as of 2-1-2021.

you may need to override line 5 on form NR which will require you to mail in the Illinois return. 

per prior year NR instructions

schedule NR Line 5: Wages, salaries, tips, etc.
Enter the amount shown as Illinois wages on the Illinois copy of the
W-2 forms you received while you were a nonresident.
Do not include any Illinois wages you received while
you were a resident of Iowa, Kentucky, Michigan, or Wisconsin.

 

 

The Illinois-Iowa reciprocal agreement applies only to W2 wages and salaries.  It does not apply to self-employed income.

https://tax.iowa.gov/iowa-illinois-reciprocal-agreement#:~:text=Iowa%20and%20Illinois%20have%20a,Iowa%20and%20not%20to%20Illinois.&text=The%20Iowa%20resident%20should%20also%20complete%20an%20Iowa%20W%2D4.

 

If your wife had self-employed income in Illinois, it is taxable by Illinois, as well as by her home state of Iowa.  She'll be able to take a credit on her IA return for taxes paid to IL on the income taxed by both states, so she won't be double-taxed.