How can an overstayed F-1 visa holder pursue an EB-5 visa option?

USCIS Policy guidance indicates that F-1s do not accrue unlawful presence until USCIS or the immigration court issues a denial, so you should be able to consular process. But I suggest a consultation before departure.

It is best that you have a consultation with an immigration attorney. Students who are admitted in F-1 status usually have an expiration date set as D/S or duration of status. If a student overstays once their school program ends, they may not accrue unlawful presence as a result of the D/S stamp or until USCIS finds that they are inadmissible. This may mean that, generally, if a nonimmigrant has not accrued unlawful presence then upon their departure they may not trigger the 3 and 10 year bars to readmission. To understand whether this would apply to you, you need to have a consultation with an immigration attorney who can review your personal records.

Your question raises more questions: did you ever apply for a change of status (to any status) while in the US through an employer or on your own? Did USCIS issue a finding of status violation? Under the law, an entry in F-1 has generous protections for overstays but it cannot be assumed for every case. So EB-5 may be an option and you would need to consular process the residence visa.

If there was no finding that you are out of status, you can leave the U.S. and there should be no unlawful presence bar.