I am looking for a solution for shifting signal in 0V to 5V range to -2,5V - 2,5V range. I can design a solution for AC with filter - where I remove the DC offset by a RC filter and add amplification (compensation). But I need a DC solution. Any tips?
You can use an op-amp, in a non-inverted summing configuration as I've illustrated in circuitlab here. You would simply need to provide the -2.5V for V_offset (for example using a voltage divider, precision voltage reference, or whatever). If you run a linear DC-sweep of Vin from 0 to 5V you'll see that Vout varies linearly from -2.5 to +2.5V. I've included an image of the circuit here for completeness.
Quite often, if you examine the use of the +/-2.5V signal, you may find you don't need to : you may be able to generate a local "0V" signal (which is really 2.5V DC) and leave your input signal unchanged. The local 0V reference can be as simple as 2 equal resistors and a decoupling capacitor; or if you need to draw significant current from it you can buffer the same circuit with an opamp.
Whether you can do this depends on your application. But if it eliminates a power supply it's worth considering.
A reversed-biased zener diode makes a simple voltage source, which you can subtract from your input by putting it in series with it:
With the output buffer, R1 can be pretty big to avoid loading the source too much, but you must keep R1 small enough so that the current is sufficient to keep the current in Z1 high enough to get a stable voltage. See your selected diode's datasheet for that current. Without the output buffer, your selection of R1 will be dependent on the impedance of the devices connected to the inputs and the outputs.
Of course, zener diodes aren't the most accurate voltage references, and the voltage varies a little with current, but if your application doesn't demand that accuracy, it's hard to get simpler than this circuit.