7805currentvoltage-regulator
This is the datasheet of 7805 voltage regulator produced by "Continental Device India Limited".
Question:
Most voltage regulators (especially LDO types) require a capacitor on the output for stability, and it will usually improve transient response even for regulators like the 7800 that may not strictly require it. An input capacitor is usually required to reduce source impedance.
It is impractical to make capacitors more than tens of pF (or so) on an inexpensive chip- they take up too much expensive silicon area, and external ceramic or electrolytic capacitors are very cheap in quantity. That is not in the cards. And the capacitors actually provide energy storage so it's not something that clever circuitry can substitute for.
The values are compromises that make sense based on the chip stability behavior at different load currents, and also what caps were common when the datasheet was composed (that might be 35 or 40 years ago for the 7800 series). It is almost always acceptable to use a larger capacitance on the input, and usually acceptable on the output, however there may be minimum/maximum values on the capacitor ESR- the equivalent series resistance. In some cases a capacitor that is too ideal may cause the regulator to oscillate.
Most modern regulators will indicate what values and types of capacitor are acceptable, so reading and understanding the datasheet is all you need to do.
Simply use an SMPS replacement for the 7805. These are readily available ...here's a commercial variant that plugs into the TO 220 pinout you have with no heatsink required:
There are many variants available on Ebay or from Digikey/Mouser.
Best Answer
Those are two very different things measured in different situations.
Short circuit current is what comes out from the regulator when its output is shorted to ground, so the output voltage is zero. So regulator protects itself by limiting current.
Peak output current is the maximum current what the regulator can drive into load when output voltage is regulated to the nominal 5V voltage. This requires that the input voltage and temperature are within some optimal range, or there will be less current.