Phase 10 how to play on after completing 5 and 3
TLDR


Based on the wording of the rules you won...


So the rules say that a player is the winner if:


  THE WINNER: The first player to complete Phase 10 at the end
  of a hand is the winner. If two or more players complete Phase 10 in the same hand, then the player with the fewest total points is the winner. In the event of a tie, the players that tied replay Phase number 10. The first one to go out is the winner. 


Looking at this specifically according to the wording it reads that once a hand has ended the first player to have completed phase ten has won. It does not say the winner finished the hand or that the winner finished without cards. It simply says that at the end of a hand the first to have completed the final phase is the winner.

In addition, consider this statement:


  If two or more players complete Phase 10 in the same hand, then the player with the fewest total points is the winner.


This would mean that a hand has ended and two or more players have finished the final phase. One may have cards left and the other may have gone out. Or both players finished with cards and someone else has gone out to end the hand. Either way they both finished in the same hand on phase 10.

According to the rules, the game has ended for all players that did not finish the last phase and the last players now must determine who won. First, the player with the lowest number of points is the winner. If that is not possible then the tying players play the final phase again and the first to go out is the winner.

Since the hand ended and you were the only player to  have completed the final phase, you win by default.