it will guarantee that it will go into 1st and you can see if it still grinds 1st. if not you will need to play with it till it goes into all the gears. if it grinds first after doing that then you got more issues.
or get the plate then for uses to center the shifter. (or a 2nd person that can hold it dead center.)
i believe its cable related because your having issues with 1,3,5 so my bet is its not pulling the shift tower far enough. and adjusting it like i said chances are your issue will then be hard getting into 2,4,R. then you need to find a happy middle point, but bad shifter bushings will make that almost impossible