¹Definition: A skyscraper is a sort of deformed X-Wing; the corners form a lopsided rectangle (a trapezoid.) Similar to the X-Wing, a Skyscraper has two parallel binary lanes. But only one of the cross-lanes lines up. The two cells in the lined-up cross-lane form the "base" of the skyscraper, and the other two cells form the sloped "roof". Of course the skyscraper can be upside-down or laid on its side, so the "roof" isn't necessarily above the base.

²

³Look For: A candidate that appears exactly twice in a Lane. Then look for a parallel Lane with exactly two of that same candidate in its Lane, where one of their cross-lanes lines up. (If both cross-lanes line up, it's an X-Wing, not a Skyscraper.)

⁴Consequence: In cells where the roof cell's houses overlap, the candidate can be erased.

⁵Why it Works: In our example, using the same reasoning as the X-Wing, we know that one of the roof cells must contain the candidate 5.
[This is because rows 3 and 5 are binary lanes: with only two of the candidate on a row, one must be true (a 5), and the other false (not a 5.) And since the 5's in column C line up, one would cancel the other out, so at least one of them must be false, leaving the other candidate in its row to be true in the roof of the Skyscraper.]
In fact, since roof cells don't line up, both cells in the roof could solve to a 5, while neither of the 5's in the base column (C) need to be a 5.

So, D3 and/or E5 will be a 5. You can see that if D3 were a 5 it would eliminate 5 from both E1 (within its Block) and D4 (within its column.) You can also see that if E5 were a 5 it would eliminate 5 from both D4 (within its block) and E1 (within its column). So, whether a 5 eventually goes in D3 or E5, any 5's existing in the overlap of the two houses (E1-E3 & D4-D6) can be erased.

⁶Turning to an example from a real puzzle, scanning for candidates that occur exactly twice in a Lane, we find 6's on row 4. Looking for a parallel row of 6's, we find row 7.

⁷The base of the Skyscraper will always be the cross-lane where the candidates line up. If the binary lanes you found were rows (as in this case) then the base will be a column. Conversely, if the binary lanes were columns, then the base will be a row.

⁸Knowing the base, finding the roof is a no-brainer: the roof is the two cells of the Skyscraper that are not the base.

⁹Now that we have identified the roof of the Skyscraper, we just have to visualize the houses of the roof's cells, and then see where these houses overlap (shown in darkest gray: cells G7-G9 are in G4's column, and in I7's block; cells I4-I6 are in G4's block and in I7's column.)

¹⁰Finally, we search the overlapping areas for the candidate, and erase it where found.

The Base is in column A.