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I don't listen to much classical; however, I recently found this beautiful work by Chopin. I am wondering if you could help me explain a particularly amazing moment in the piece. Please refer to minute 26:00-26:10 for reference in the attached youtube clip. Below is an image of the section:

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The first five (5) bars have a minor quality to them and sound quite hopeless. But then the sixth measure comes out of nowhere with that G-flat -> D-flat chord sequence that just feels like a breath of fresh air.

Could you explain this to me? My first guess would be that in the first 5 measure we are in the relative minor of the key and then move to a PAC in the relative major key, thus bringing the positivity. But the key with 4 flats is A-flat major (D-flat being the subdominant chord), so that doesn't really seem to be it. The G-flat -> D-flat change is a dominant-tonic one, but not in the current key. So were we modulating to D-flat major just for a moment?

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Your intuition is correct; it's just a move to the relative major! But we can clear up some details.

Although the key signature is four flats, the music is really in B♭ minor for these first few measures; it certainly cadences in that key at the end of the first system.

Following this B♭-minor chord, a sudden appearance of G♭-major shifts the mood. You say that G♭ to D♭ is a dominant to tonic motion, and you're mostly there! Dominant to tonic is a descending perfect fifth, and G♭ to D♭ is an ascending perfect fifth. As such, I hear this progression as a plagal IV–I motion in the relative major of D♭ major.

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Dolce begins in Ab: I - viidim7 leading to the relativ chord (Bbm) of the subdominant (Db) by Ebm-F7 => Bbm which is (iv-V7) ii and from here he just uses the well known half-cadence to F (the V of Bbm): i-VI-III-iv-V. (Bbm-Gb-Db-Ebm-F).

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