It might sound like an easy question. What makes me confused is that the independent variable takes any values between 0 and 5 including the numbers such as 1.987. So, I am not sure if I should consider it as an ordinal variable.
follow the lead of Demetri and rescale the variable to be between 0 and 1. Then you can use beta regression but you also have the fractional logit model in your arsenal, see here.
I hope this helps.