When you play poker as long as you have your strategy set with all of your outs identified then you will do fine. If you want to play hardball then so be it. However what you are trying to do is apply your own speculation about how the bank “should” behave based on your own logic. The problem is that the banks are in this situation due to greed and not logic.
So it would follow then that it could be very logical for the banks to continue to be short sighted and act in a greedy manner.
If you lose the home over the 5k there are plenty more homes that you will not miss out on.
I would say that your chances are somewhat less then 50/50 but you will not know if you do not try. My personal experience is that it has been pretty difficult to get the bank to move on the numbers especially after they have gone through the process of getting the approval.
Let me ask you, how long has it taken to get the approval for the line release?
If you do ask for the 5k then how long will it take them to process that request?
At any rate like I said, don’t be afraid to ask. Weigh your risks. Think about it this way… suppose it takes them another several weeks to approve your request. However in that time loan rates go up and you end up locking in a rate 3/8 of a point higher then you would have locked into had you been able to close earlier because of the delay. So now you get 5k in hand but in a several years you will pay more then that in interest. This is all theoretical and indeed in that same time rates can go down further and you would be BETTER off! Just try to consider all angles. It may not hurt to ask, but if you really love the home consider all possible outcomes. If you just like the deal but are just so so on the home, then go for the 5k.
I would caution that you should be buying the home cuz you love the home, not just because it is a good deal because there will be plenty of good deals.