we have a 15 acre lake we have to do this to and your choices are pretty limited.
your cheapest is to drain it and dig it out with a backhoe, if it is dry enough should be easy enough to do
and should be well below 5k
just make sure you have dried it out, it makes good soil enhancer
If you do the pump dont forget after you use the pump - EBAY and get back 1/2 of what you spent