I, like @Justin_Barrett, am having a little trouble wrapping my head around what you are wanting to do – and we are trying to understand your use-case because it seems there must be a better way to accomplish your end goal, although, perhaps, it doesn’t look exactly the way you are envisioning it.
I think that is likely true (there is a better approach than what you are suggesting), but since I don’t fully grasp what you’re trying to accomplish, I’ll give you the short answer to your explicit question…
You will need 4 separate columns in Table 5 – one for each other table that you want to be able to link to. When you define a column as a “Link to another record” column, you have to specify the table the records will come from. You can’t specify multiple tables for one column. Airtable is basically reserving that column for “Links to records from Table 1”; and reserving the next column for “Links to records from Table 2”; etc.
So, Table 5 will end up looking rather inelegant. You can smooth it over a little by pulling the title from whichever of those 4 fields is actually being linked into your Primary field, so that you can always see the name of the record you were linking to in the same column (the Primary field). But you still have to be conscious of which column you attempt to create the link in, and if you are only ever linking 1 item to a record in Table 5, you will always have 3 empty columns in each record in Table 5 (one for each Table you are not linking to).
Hopefully that gives you a sense of how to accomplish what you want – but I’m also hoping it encourages you to rethink how you might be able to accomplish your goals, as this solution may feel a little inelegant.