As we can see, this overload of the GroupBy extension takes a delegate which is used to enumerate the tableJson and generate a key for each item.
Items that generate the same key will be grouped together and returned as an IGrouping . There is no special treatment based on the type of the source. This doesn't do anything different, whether you have an array of int s or an array of complex objects.
So, if you want to group by a combination of columns you need to provide a function that returns a unique, repeatable, key for that combination of columns.
This can be simply achieved by compounding those columns into an anonymous type, which has a built in implementation for equality and hashing that suits our purposes, like in this answer .

var groupedTableJson = tableJson.GroupBy(x =>
    new {
        FirstColumn: x["FirstColumn"],
        SecondColumn: x["SecondColumn"],
        FifthColumn: x["FifthColumn"]
    });

Your answer is almost right but, you don't provide names for properties of your anonymous type. However, since you don't explain what "does not work", it is hard to be sure.