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I'm looking for a systematic approach to simplify circuits like the one in the picture below. The solution to this problem unfortunately does not address how it got there and simply states "its obvious that..".

circuit

My current "approach" is to mentally wrap the lower part of the circuit (connected to the source) over the rest, but that seems to me to be a very inefficent and error-prone way.

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If you follow the stream from the source, then you have to choose between $R_4$ and $R_5$, so those two are in parallel. $R_5$ then goes back to the source and is done. From $R_4$ you then have to choose between $R_1$, $R_2$ or $R_3$ so those three are in parallel.

So how I would visualise it is that there are two parallel main loops. One has only $R_5$, the other one has $R_4$ in series with a parallel connection with $R_1$, $R_2$ and $R_3$.

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