How soon can I poke a potential PhD advisor for a response if contacting them about an advertised position? There is a PhD programme I recently found which matches my interests very closely but with a deadline in five days. It doesn't require me proposing my own research, instead asking me to choose from a list of available projects. The application instructs me to contact the professor who advertised the project before I proceed with the main application.

I've sent that potential advisor a carefully-crafted cover letter and CV a few days ago but got no response. Normally I'd not try to send a second email so soon but I'm feeling increasingly pressured on time given the few days there is until the institution-wide deadline. I am find with filling in the forms at the late notice but I'm concerned my referees might not be as happy about copy-pasting the references they have already wrote for me.

I wanted to see what other people think on the subject - would it make me a disservice to contact the potential advisor again in a couple days or should I just give him a time to respond in his own time (potentially after the deadline or never)?
I do not think it will be disrespectful to send a follow-up email. I would craft it in a way that shows you value his/her time, but also demonstrating that you have an immense interest in the project, which is why you are reaching out. I would have a backup plan just in case.