Hey everyone, this is from a recent game I played on chess.com

I sacrificed a lot of material and ended up exposing his King.  In the actual game I ended up with a winning position, but I was wondering if there were any defensive outs from my opponent?  Or if I could have won more swiftly?  I had a couple minutes left on the clock to work it out, but because of the time increment, I knew I could settle for a dominant endgame position without risk of losing on time.

Rd7+ Qe7 Qe5+ looks much stronger

Rd7+ Qe7 f6+ is your best move. all of blacks 3 responses lead to mate:

1) ...Nxf6  Qxf6  Kg8  Rxe7  Rxe7  Qxe7  h6  Bf6  Rh7  Qe8#   fairly straight forward with black's moves all made to prevent impending mate.

2) ...Kf7  Pxe7+  Kg7 (Ke6 is met with Rd6#  and  Nf6 is met with Qxf6  Kg8  Bh6 and followed by an easy bishop/queen mate)

once black's plays Kg7, play continues with Rd8

in this position, you'll find black is unable to move any pieces without white quickly checkmating.

if black exchanges rooks, a 2nd queen is promoted and the game ends very soon after.

if the knight is moved anywhere, white plays Qf6+  Kg8  Rxe8#

if any other pieces is moved, white plays Qf8+ (white will have to find mate on Qf7 if black moved his h-pawn to give himself an escape square)

black's last option was 3) ...Kf8   this is also met with Pxe7+  Kg7  Rd8  etc... and the board stands as it did before.

there it is. thanks for the problem

Thanks for all the solutions guys!  I figured there was bound to be mating opportunities there.

I wonder if you saw this one:

That was quite pretty, riuryK!  I wish I had seen it.

Yes, it is very pretty but requires black to play the obvious mistake kg8. Since his position is lost anyway that does not seem too unlikely though.