Though it seems that the company is unfair for not standardizing the qualifications to be a regular employee, however, it is still a valid exercise of "management prerogative" to whom the company choose to be a regular employee.
You dont have a valid reason/point or cause to demand that you be promoted to a regular status, because:
1. Being a project employee, you are considered as a REGULAR employee during the duration of the project. (Im just wondering, are you really a project employee?, how long is the project will take?, i mean the duration thereof?)
2. The right to promote is vested to the employer, that is one of the powers included in the term "management prerogative"
3. Lastly, Your Direct employer is the agency and not the company.
** Since you were employed by an agency, i believe that you are a contractual employee, whose contract is renewable by your agency and the company without you knowing it.(This is only my theory, after you said that you were a project employee for 5 yrs.)