A few days ago, when I went to a shop to get my compression measured (on a Civic '90 DX), the guys told me my starter is spinning a bit too slow. On a side note, it takes at least 4-5 rotates to start the engine... something like "cg-cg-cg-cg-WOOOM". Now I'm wondering if this is something I could fix myself? Because the shop is asking 100$ just to take a look at it.

On a (second) side note, the car is maintained, oil is changed recently, battery is OK and so is alternator (measured it both using multimeter). Spark plugs, wires, distributor cap, rotor, fuel filter, everything is recently changed and working fine. The car had this problem for at least 4 years now.

I would think if there was a problem with the starter, it would have gotten worse over 5 years. Work on the connections, making they are clean and tight both from the battery to the starter, and from the battery to the engine. Always disconnect the negative terminal to the battery before working on the positive cable.

The connections inside the solenoid could be bad too, but harder to check. You could have somebody turn the engine over while you checked the voltage at both solenoid terminals. If it drops, the solenoid is bad and should be replaced.

I would think if there was a problem with the starter, it would have gotten worse over 5 years. Work on the connections, making they are clean and tight both from the battery to the starter, and from the battery to the engine. always disconnect the negative terminal to the battery before working on the positive cable.

The connections inside the solenoid could be bad too, but harder to check. You could have somebody turn the engine over while you checked the voltage at both solenoid terminals. If it drops, the solenoid is bad and should be replaced.
Yepo that would cause it :)