nope , not good. I tested in other simulator that circuit with the transistor, which very much resembles your much simpler version and I applaud its simplicity, I like it very much actually, more than mine.
But the problem with both circuits here is that Pressed button !!! As long as I am keeping it pressed, it will "count" 0V ! Which is not good. So if im counting 10s with the button pressed down to 0V, the circuit will stay to 0V 10s. WHen I release the button, it will count another extra 50ms based on the cap and res values that I chose and reach 5V. So this behavior is NO BUENO !
What I really need is like this: Press ONCE the button and keep it pressed. But the circuit will not stay at 0V. It will jump from 5V to 0V in the moment the button made the contact, count internally those 50ms, and rise up to 5V by itself, while my button is still pressed. When I release the button from its contacts, the circuit still remains at 5V, unchanged. Only when I press the button again. and at the very first contact , the whole logic repeats again. Clear now?
I am trusting the good old 555 timer to do it. But... I didnt actually stay down to think about it. I only figure out how the logic should be, the one I just described so far.
Remember this is waaaay a SIDE mini-project or dare. Haha. Not at all the main quest Im in. Its a cute side quest. A curiosity.