Create line from points with specific direction

[LienPham1]

I have multiple points and the distance of each points is nearly 2.5 meters.

How can I generate lines with in specific direction, (the red colour lines on the picture) from the points which has distance approximately 2.5 meters and each line should have the distance of approximately 5m (red arrow on the picture).  The points which have distance with other much less than or larger than 2.5m should not be used to generate lines. Could you please let me know which tool in ArcGIS Pro can I use to do the task

I use to do this task?

[DanPatterson]

Are the points sequential?

The only available builtin tool is

Points To Line (Data Management)—ArcGIS Pro | Documentation

[LienPham1]

Hi Dan, No  the points are not sequential

[DanPatterson]

I would recommend the Near tool, but there are too many areas where points along an apparent 'line'

deviates greatly from the 2.5 within spacing and 5 between spacing.

If you have an attribute that you can identify the point sets by, then there might be a combination of cursors or numpy arrays to split the dataset by, then perform a lexicographic sort per "line".

[LienPham1]

I have modified my question. You are right Dan, if some points have the distance with other less than or much larger than 2.5  within spacing and 5 between spacing should not be used to generate line. 

Could you please explain more your methods? I also attached to my question my data.