OK, this is not complicated.
A 7805 regulator has a 2V dropout voltage, meaning that once the input voltage is below 7V the regulator cannot regulate at all, the input voltage variations are passing directly through to the output. If you notice in the datasheet all the performance data is measured with an input voltage of 10V. A minimum input voltage of 8V should be OK, but really the minimum input voltage, meaning at minimum AC line voltage (meaning 207V in Europe, 230V nominal -10%).
You can see clearly on your scope picture (and I have highlighted to make it even more obvious) that the input voltage falls below the minimum dropout voltage.
The points where the input voltage falls below that 7V line I have marked correspond with the points in the output 5V that have the drooping response.
The transformer you chose for the 5V supply is not appropriate, it needs to be higher voltage (and rated appropriately to supply current to the multiple units).
When I asked earlier what was the current draw for the 5V supply your reply was that you don't know. That indicates that you do not have enough basic information to choose an appropriate transformer, so as a bare minimum you should measure the current consumption of the different power supplies, and check the original transformer to see how it was rated to make sure that you do not purchase another inappropriate transformer.
Presumably you should double check that the higher voltage transformer is appropriate as well, it is possibly barely functioning properly.