Would such an arangement work?
If I'm reading your schematic correctly, no. I think it's something like this:
simulate this circuit – Schematic created using CircuitLab
There are a couple problems here. Firstly, each of those LEDs has a forward voltage. If you can't provide this voltage, then the LED just won't turn on. Forward voltage depends on the color of the LED among other things, but for an ordinary RED LED, it's in the neighborhood of 2V.
You have five such LEDs in series, so you need at least 10V to turn them on at all. But you have a 5V battery, so that's not going to work. You'll need a battery with a higher voltage, or a couple batteries in series.
Secondly, you have six resistors in series with the LEDs. While this won't prevent the circuit from working per se, there's no reason to do that. Since this is all one series circuit, the current is the same everywhere in it. How could it not be: there's no other place for the current to go. Those five 470 ohm resistors are equivalent to one 2350 ohm resistor (470*5). You could save some parts by using just one resistor, and probably it's not the right resistance.