You can perhaps see the logic of why it's suggesting to index the invoice date; it's done some calculation on the number of rows you want out of the number of rows it thinks there are currently, and it appears that the selectivity of an index on that column makes it worth indexing. If you want 3 rows out of 55,000, and you want it every 5 minutes forever, it makes sense to index. Especially if the growth rate of that table means that next year it'll be 3 rows out of 5.5 million.
The include recommendation is perhaps more naively recommending associating sufficient additional data with the indexed values such that the entire dataset demanded from the master table can be answered from the index, without hitting the table - indexes are essentially pointers to rows in a table; when the query engine has used the index to locate all the rows it will need, it then still needs to bash the table to actually get the data you want. By including data in an index you remove the need to go to the table and it's sensible sometimes, but not others (creating many indexes that essentially replicate most/all of a table data for seldom run queries is a waste of disk space).
Consider too, that the frequency with which you're running this query now, in a debug tool, is affecting SQLServer's opinion of how often the query is used. I routinely find my SQLAzure portal making index recommendations thanks to the devs running a query over and over, debugging it, when I actually know that in prod, that query will be used once a month, so I discard the recommendation to make an index that includes most the table, when the straight "index only the columns searched" will do fine, no include necessary
These recommendations thus shouldn't be blindly heeded as SQLServer cannot know what you intend to use this, or similar queries for in the real world applications. Index creation and maintenance should be done carefully and thoughtfully; for example it may be that this query is asking for this index, another query would want an index on a different column but it might make sense to create an index that keys on both columns (in a particular order) and then in whichever query searches on the column that is indexed second, include a predicate that hits the first indexed column regardless of whether the query needs it
Example, in your invoices table you have a column indicating whether it's paid or not, and somewhere else in your app you have another query that counts the number of unpaid invoices. You can either have 2 indexes - one on invoice date (for this query) and one on status (for that query) or one on both columns (status, date) and in this query have predicates of WHERE status = 'unpaid' AND date between... even though the status predicate is redundant. Why might it be redundant? Suppose you know you'll only ever be choosing invoices from last week that have not been sent out yet, so can only ever be unpaid.. This is what I mean by "be thoughtful about indexing" - you know lots about your app that SQLServer can never figure out.. By including the redundant status column in the "get invoices from last week" query (even though status is logically redundant) you allow the query engine to use an index that is ordered first by status, then by date. This means you can get away with having to only maintain one index, and it can be used by two queries
Index maintenance and logic of creation can be a full time job.. ;)
