Ripple in my power supply
A fullwave rectified power supply below  will have ripple due to charging and discharging of the bulk capacitors.

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where the ripple voltage is $$V_{pp}=\dfrac{I}{2fC}$$
and I is the load current, C is the capacitance and f is the mains frequency.

So as the load current increases so does the ripple. To reduce this ripple you need to increase the bulk capacitance.

This is followed by a 7805 which should reduce that ripple by its RR (ripple rejection), which is about 60dB for the 7805. So Vpp in your first calculation should be reduced by about 1000.

If this is not happening for you check the dropout of the 7805 is respected, i.e. you need the input to be at least 2.0V more than the output i.e 7V min and this needs to be the case even under full load because the transformer output voltage will reduce under load.