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Okay I treat water for a living.
Lime-- found usually as calcium or an elemental combination of calcium hydroxides/chlorides or carbonates. It is dissolved, in solution, a filter will not remove. Manganese and iron are also very common.
Picture, sugar dissolved in water, pass that sugar water through a filter, and on the output side of the filter you still have sugar water. On the other hand--- Picture a teaspoon of sand stirred up in a glass of water, pass the sand/water through a filter and on the output side of the filter NO SAND, larger than the nominal micron rating of the filter.
Now all kinds of qualifications here----
Reverse osmosis filter-- will actually produce pure water (demineralized), most common application of this process is desalanazation (spl remove salt).
Calcium and lime will precipitate (make a ring in the bowl) when exposed to heat or air, as your water passes through your pipes it gets warmer, and a slight amount of calcium will precipitate when transiting the filter.
$5000 price tag?
What I have on my whole house system is a water softener with a prefilter (to remove suspended solids that could foul the softener resin). Cost me about $500 and I installed myself, so total cost about $650. Yes! I do have to add salt sodium chloride or potassium chloride. This removes all elemental impurities. But this is not a filter it is actually an ion exchange system, ----- a deionizer 
Sears, Home Depot, Lowes, Do-it Center hardwares, and the good old Culligan Man sells them.
By the way have you actually had your water tested? Lots of stuff will produce crust when water evaporates.