The search in the Open dialog box is controlled by your operating system, NOT by InDesign. What operating system are you running?
Software OS X 10.9.5 (13F1077)
Processor 3,4 GHz Intel Core i5
Memory 24 GB 1600 MHz DDR3
Graphics NVIDIA GeForce GTX 775M 2048 MB
It is the search/place function IN indesign, so not spotlight or search on desktop.
As Steve already told you, that function is being done by the O/S.
And is there a way to solve it?
This question has been asked before. For many of us (the majority?) who use Mac OS X recent versions, we have no problems finding InDesign files in the Open dialog box using the Search feature (which does use Spotlight in the background). Here's a search I just did:
I happen to be using Yosemite, Mac OS X 10.10.3, but I had no problems with Mavericks.
It could be that you have a third-party utility which is interfering. It could be a system issue that would be rectified by using InDesign in a new user.
As I recall, in previous threads, no answer has yet been found.