How to deal with multicollinearity between a continuous variable and a dummy variable

[Da GXHI]

I am trying to run a regression with explanatory variables both continous and dummy. dependent variable continous.
I notice that one of my dummy variables is correlated to one of the continous variables and that seems to couse collinearity. I checked Point-biserial r is about 0.74.

Variable background:

reg y x1 x2 x3 x4, fe

the dummy variable is created as x1=1 if x5>threshold
x5 is not part of my regression itself. but x5 is highly correlated to x2 (pearson 0.9).
Conceptually both x1 and x2 are relevant in the analysis so I would prefer not to drop the dummy.

Any idea on how I could deal with multicollinearity in this case? I checked Factor Analysis (princeton.edu) , but couldn't understand how/ if I could use this to solve multicollinearity issue in my case.

Any suggestion is very much appreciated! Thank you!

[Carlo Lazzaro]

Da:
without any detail abiut what you typed and what Stata gace you back, the only advice is to make a choice concerning the right-hand side of your model to avoid perfect collinearity (if feasible).

[George Ford]

Try transforming x2 (natural log, etc.) to move away from the linear correlation. But the real problem is you've got nearly the same variable appearing twice.

[Da GXHI]

Thanks for the suggestions. The stata output I got initially has a negative sign where a positive one is expected (for x1). I tried rerunning in groups and it seems like this sign changes often so I guessed multicollinearity is present. Plus checking on the correlation between these two variables is high. Adding variables one by one two the regression the sign of x1 coefficient changes only when adding x2. I tried transforming x2 to natural log and the sign of x1 turns positive although not significant.