The one of suppression capacitors in the 7805's is a very interesting topic 
in itself... that values of input and output capacitors have been changing 
in the datasheets for years.
The LM340T series of regulators (of which the 7805 is a direct descendant) 
used to need one 10uF tantalum capacitor in the input and another in the 
output. Being tantalum caps  known for its flashy temperament, it drove 
some designs to very interesting failure modes. I have seen datasheets that 
put the capacitors as unnecessary and other as must-have. I feel much 
better with suppression as a must-have and with the small size of SMD 
components, it seems nonsense not to install them.

On Monday, March 30, 2015 at 7:33:57 AM UTC-3, Nick wrote:
>
> Just to re-iterate - solder a small 100nF capacitor between pins 1 & 2, 
> and another between pins 3 & 2, preferably on the underside of the PCB 
> directly to the 7805's solder pads.
>
> The symptoms you are seeing are almost certainly nothing to do with the 
> heatsinks etc - I'd put good money on this being a very common & classic 
> issue with 78xx & 79xx linear regulators whereby they break into VHF 
> oscillation and over-heat. This is extremely well documented and the 
> manufacturer's datasheets all say that the two suppression caps are not a 
> "nice to have" but are essential. Most of the datasheets actually specify a 
> 330nF input capacitor (between pins 1 & 2) but a 100nF works well too.
>
> Missing out these two capacitors is a basic error.
>
> Nick
>
>
>

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