Neat! That's a falling-block idea I haven't seen before.
(1) I didn't find the rotating-the-board to be intuitive to control, and had a strong tendency to try to rotate it back and then drop the current piece (and lose).
It might be worth trying out a control scheme where the board is always the thing that the player moves. (That is, keep the relationship of the piece and the board functionally the same, but take the piece to be staying in place -- at least horizontally -- while the 5x5 board is the thing that the player moves and rotates.) Like this:
http://www.piskelapp.com/p/agxzfnBpc2tlbC1hcHByEwsSBlBpc2tlbBiAgIDu5_7uCQw/viewRotating would still be dangerous, though, because of the way that rotation suddenly puts blocks at the top of the pit. (Like if you asked any Tetris player, "Would you like to put those blocks at the bottom of your pit at the top", the answer would be "of course not, that's really dangerous!") It may be worth trying variants that let blocks push each other down or otherwise make room for each other.
(2) One good design principle for a draw-a-random-shape game (be that Tetris or Carcassonne or even Starseed Pilgrim) is that draws are good or bad depending on your current situation, rather than inherently good or bad. (So that once you move into intermediate-level play you realize that you "make your own luck" and play so as to maximize the usefulness of any draw.) Given the goals of connecting-two-sides-of-the-board, particular pieces (the ones with a straight line) are just inherently better than others, especially a line in the direction you want to go. (Because even though you can rotate, it's invariably going to be less frequent than just moving.) And those four-way junctions are absolutely always the best piece you can have.
Maybe instead of connecting two sides of the board, and having the other sides of the board unused, all four sides could have pipes, and you're trying to connect particular ones (like blue-to-blue vs. red-to-red). If you connect correctly, the pipe explodes. If you connect incorrectly, you lose. Like in
http://www.piskelapp.com/p/agxzfnBpc2tlbC1hcHByEwsSBlBpc2tlbBiAgICegPnkCww/view , that four-way-junction is a potentially dangerous piece because it can so easily join a blue and red pipe. But meanwhile, a single-bent-pipe could be a blessing rather than a "oh no not one of these again" because it can help lead red and blue away from one another.
(Actually, that might make it hard enough that you can add back in piece rotation rather than board rotation.)
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