“For an investigator-initiated R01 application, must my project period be five years?”

No, while five years is the maximum project period for NIH Research Project Grant (Parent R01, Clinical Trial Not Allowed), you should determine your project period based on the scope of the project. You could propose a two-year R01 research project if the study’s Specific Aims and budget needs are an appropriate match. But as with requesting a budget insufficient to your project’s actual needs, reviewers may interpret an overly ambitious timeline as reflecting naivety rather than prudence.