Does PCA helps to include all the variables even if there is high collinearity among variables?

I have a dataset that has high collinearity among variables. When I created the linear regression model, I could not include more than five variables ( I eliminated the feature whenever VIF>5). But I need to have all the variables in the model and find their relative importance. Is there any way around it?. I was thinking about doing PCA and creating models on principal components. Does it help?.

• Why can’t you include more than five variables?
– Dave
Oct 31 '21 at 2:30
• Because VIF increases beyond 5 when I use more than 5 features. Oct 31 '21 at 17:50
• So VIF exceeds $5$…how does that impact your analysis?
– Dave
Oct 31 '21 at 20:24
• Doesn't it mean high collinearity in the data? So that I can't keep those features Nov 1 '21 at 1:17
• But VIF of 4.5 also means that there is (multi)collinearity. How does VIF $>5$ impact your analysis?
– Dave
Nov 1 '21 at 3:05