@HellasTechn, you seem to be ignoring the datasheet recommendations concerning the capacitor values you should use. The input capacitor is a high-frequency bypass capacitor, needed ONLY if there is substantial distance between the 12 V "smoothing" capacitor and the three-terminal "7805" linear regulator input. It assumes there is NO resistor between the linear regulator input and the raw, filtered, DC output power supply. The output capacitor is a deliberately small value selected (only if needed) to avoid changing the linear regulator characteristics when the circuit is operating normally under load.
The raw DC should be derived from a full-wave bridge rectifier and "smoothed" or filtered with an electrolytic capacitor whose value depends on the current being supplied and the allowable ripple on the input. At the peaks of the input voltage, this capacitor will charge up and then linearly discharge into the voltage regulator input until the input voltage begins to increase again. The maximum and minimum values of this pseudo-sawtooth wave form must be within the allowable input voltage ranges of the the linear regulator.
So, knowing the discharge current of the filter capacitor is linear, and knowing the constant current of this discharge (why constant? because the output voltage is constant across a presumably constant resistance load, therefore the load current and capacitor discharge current is constant), and knowing something about the period of the pseudo-sawtooth wave form (about 1/120 seconds for 60 Hz line supply), you can calculate a conservative value for the smoothing capacitor. It is only if this capacitor must be physically located some distance from the regulator that the 0.33 μF input bypass capacitor is required.
The output bypass capacitor is only recommended for noise reduction. Because the output and its load is an integral part of the closed-loop negative feedback linear voltage control circuit, you should not add large values of "smoothing" capacitors to this output, lest you disturb the feedback characteristics so carefully designed into this integrated circuit. In particular,
DO NOT add 100 μF aluminum or tantalum electrolytics between the output and ground.
Gather together and READ as many datasheets as you can find, from different semiconductor manufacturers, on the 78xxx series of three-terminal voltage regulators. IIRC, at least one of these datasheets explains why you do not want to add a large capacitance to the output terminal because it can actually cause instability in regulator operation.