Sending from Bitcoin-Qt to Coinbase I had the idea to move all of my existing bitcoins (10 BTC) from Bitcoin-Qt/paper wallet to Coinbase.

I had imported the paper wallet to Bitcoin-Qt and the balance there was 10 BTC total. For some reason, I then went and imported the paper wallet to Coinbase, and ~5 BTC was added.

At this point, Bitcoin-Qt still showed the balance as 10 BTC. I went ahead and made a transaction of 10 BTC from Bitcoin-Qt to my Coinbase address.

The result is that the transaction keeps having 0 confirmations, Bitcoin-Qt shows balance to be 0 BTC and the transaction never showed up in Blockchain. I have no idea where the "missing" 5 BTC are and what to do. I realize that a double spend might have occurred as 5 BTC was already imported to Coinbase from the paper wallet and I tried to send 10 BTC from the Bitcoin-QT.

Here's the Coinbase address https://blockchain.info/address/1GeQeHnJEnKfcfWonGCrj52kChyXqib5sC, and you can see the that the 5 BTC import from the paper wallet went through.

What's the solution here?

Here's how Bitcoin-Qt's transaction history looks like:
Addendum: It looks like the coins have been found; just quoting the relevant solution from the external thread so we have a complete answer on record. Long story short, the problem was as we suspected: the paper wallet did not contain all of the change addresses from the 5btc of transactions that had occured since tge import. Simple fix: 


  I started the client with /Applications/Bitcoin-Qt.app/Contents/MacOS/Bitcoin-Qt -salvagewallet. It's still syncing with the network, but it looks promising as it's now showing a +4.9315 balance!




Ok, I'm beginning to piece together what happened now. 


At least according to your blockchain links, you initially received 10 BTC via 3 transactions, at the 1Fr3p address then spent 5 on 17 april. So that particular address only had 5 remaining at the time of the import to coinbase. 
When you import rather than send, the coins will still show in both wallets;  if you send them from the old one after that this will not update in the new wallet because of change addresses.  Importing != spending. 
You will additionally need to import the change addresses that have been created since using bitcoin-qt to coinbase for everything to sync correctly.  Check out this thread.  
As far as fixing the crazy transaction, I'm not sure what to do there.  Hopefully when you finish importing everything it will manage to work itself out in the client?  Don't send anything else from the old wallet again--once you can use  the coins  available in the coinbase wallet, send from there only. 
If you want to use qt client again, create a new wallet for all transactions moving forward. 


update
What do you know about these transactions from your link in the comments?  Your client is only showing the -.01 portion of those tx but the remainder seems to be what's missing...