How can I apply for a TN visa while my EB-5 I-526 is pending?

Best to do TN first and then I-526 if you have not filed and set up the I-526 for consular processing (you can later change to adjustment) to show your nonimmigrant intent.

If you need to work in the U.S. soon, then you could obtain TN status. If you have been in TN status in the U.S. for an extended period of time, then you could file an I-526.

It is recommended you apply for and get admitted on TN. Keep in mind TN status requires showing a nonimmigrant intent/ties to your home country. When you file an EB-5 immigrant petition (I-526), it is advisable to indicate consular processing. You may apply for AOS, including employment authorization and advance parole concurrently with I-526 if eligible. Discuss your options with an experienced immigration attorney.

The TN visa does require temporary intent so having the petition on file is an adverse circumstance. However, it is up to the officer and if you can show you have no intent to adjust status, the officer may decide to issue the TN provided you show you have not permanently severed your ties with your home country.

It would be advisable to obtain TN status prior to filing your EB-5 petition due to the "non-immigrant" intent required for TN status. That being said, it is possible to obtain TN status after filing Form I-526 - if you are filing Form DS-160 you have to confirm that you have a pending I-526 petition but you can also state that your present intent is to work temporarily in the U.S. and once your I-526 petition is approved you will complete consular processing abroad.