I have a motherboard Hi-Fi a70u3p (http://www.biostar.com.tw/app/ru/mb/introduction.php?S_ID=773) and I need to buy an intel core i5 6600 or equivalent processor. Does this motherboard support this processor model? If not, then advise similar processor that this motherboard supports.
Your mainboard takes AMD Socket FM2/FM2+ CPUs. That's a fairly old socket, designed for AMD's APU-series processors, so modern high-power CPUs aren't available for it.
The closest you're going to get to the performance of an i5-6600 is the A10-7890K, currently available from Newegg for $150. It benchmarks about 10% slower than the i5-6600 for single-threaded work, and about 30% slower for multi-threaded. This may or may not be sufficient for your purposes.
As Andy mentioned in the comments, this is an old AMD board. The FM2 socket is a few generations old at this point. You're going to have to find a used CPU that is compatible with the board, as AMD no longer manufactures any CPU that is compatible with it.
You can find a list of supported CPU models by looking for your motherboard's user manual online, or viewing a compiled list on the wikipedia article regarding the FM2 socket, or by using a site such as www.pcpartpicker.com. Good places to look for old hardware are Ebay and a community on Reddit called "r/hardwareswap" (without quotes).