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Is it possible to create a custom sort that would ignore the first 5 numbers and dashes in column 1?

No. At least not without custom programming ("macos").

Is it possible to sort column 2 in a way that matches their partners in column 1 (possibly with custom sort?)

No. (See above.)

Column 1 can NOT be modified in even the slightest way... however, column 2 can be modified in literally ANY way.

We should never modify original data, exept for cases where the modification itself is what we want to achieve.

What to do then?
Use a helper column. It must be "in contact" with the first column and (probably) its accompanying data.

See this attached example.

(Quoted from OQ:) Is it possible to create a custom sort that would ignore the first 5 numbers and dashes in column 1?

No. At least not without custom programming ("macos").

(Quoted from OQ:) Is it possible to sort column 2 in a way that matches their partners in column 1 (possibly with custom sort?)

No. (See above.)

(Quoted from OQ:) Column 1 can NOT be modified in even the slightest way... however, column 2 can be modified in literally ANY way.

We should never modify original data, exept for cases where the modification itself is what we want to achieve.

What to do then?
Use a helper column. It must be "in contact" with the first column and (probably) its accompanying data.

See this attached example.

(Quoted from OQ:) Is it possible to create a custom sort that would ignore the first 5 numbers and dashes in column 1?

No. At least not without custom programming ("macos").

(Quoted from OQ:) Is it possible to sort column 2 in a way that matches their partners in column 1 (possibly with custom sort?)

No. (See above.)

(Quoted from OQ:) Column 1 can NOT be modified in even the slightest way... however, column 2 can be modified in literally ANY way.

We should never modify original data, exept for cases where the modification itself is what we want to achieve.

What to do then?
Use a helper column. It must be "in contact" with the first column and (probably) its accompanying data.

See this attached example.

example.

(Editing with respect to th comment below:)
I only rememberone helper column labeled "SORTINGCOMPANION1_HELPER" and introduced in sheet "OriginalDataCompanion1Added". The reslults shown there are returned by the formulas contained in the cells. Disregarding the amount of interactive handling and the error risks coming with that, you might also do it with 'F&R' applied to a copy of the original data. I prefer the formulas in such a case.
New demo attached.

(Quoted from OQ:) Is it possible to create a custom sort that would ignore the first 5 numbers and dashes in column 1?

No. At least not without custom programming ("macos").

(Quoted from OQ:) Is it possible to sort column 2 in a way that matches their partners in column 1 (possibly with custom sort?)

No. (See above.)

(Quoted from OQ:) Column 1 can NOT be modified in even the slightest way... however, column 2 can be modified in literally ANY way.

We should never modify original data, exept for cases where the modification itself is what we want to achieve.

What to do then?
Use a helper column. It must be "in contact" with the first column and (probably) its accompanying data.

See this attached example.

(Editing with respect to th comment below:)
I only rememberone remember one helper column labeled "SORTINGCOMPANION1_HELPER" and introduced in sheet "OriginalDataCompanion1Added". The reslults shown there are returned by the formulas contained in the cells. Disregarding the amount of interactive handling and the error risks coming with that, you might also do it with 'F&R' applied to a copy of the original data. I prefer the formulas in such a case.
New demo attached.