Solution 5A Beginning with the push of W1 is correct! The only conceivable response is the block of B2, but that leaves Black with the two dangerous cutting points at “a” and “b!
If Black then gives atari to W3 via B7, that would allow the counter atari of W6, followed by losing the corner to White. So Black played B6, allowing W7 as shown.
Then with the second cut of W11 followed by the sequence thru W19, White makes a nice profit, while Black has to go back to secure his life in the corner with B20 while leaving his 7 outside stones with bad shape and uncertain prospects. So White stands much the better here.