Hi,
If you want to dim your lamp you will need more than a SSR , Arduino and a 5V supply.
You need to research how an AC lamp is dimmed, it is called phase control and this link will help.
There is an SSR (wired correctly) and the 5 volt power supply (wired incorrectly).
Where are you doing phase control (dimming) in this schematic? The SSR shown does not dim, only on and off control. Please clarify what you want to do, a capacitor has no place in the schematic shown.
And that's not what your examples do either.
The example you show in that video clearly says wireless dimmer module.
It relies on a WiFi signal which could be controlled by an Arduino or any other controller.