It does mean five rounds basically. The words in front of 五番勝負 indicate that they're competing in the Hulic Cup for the Kisei title.

Mainichi Shimbun (Japanese):
７タイトルの合計獲得数８１期目に挑戦中です。現在進行中の棋聖戦五番勝負で中村太地六段（２４）の挑戦を受けており、これまで２連勝。

Mainichi Shimbun (English):
He's now playing a tournament with his sights on his 81st championship title. He is facing off against sixth-dan ranked Taichi Nakamura in a five-match game for the Kisei title, with two match victories so far.

This is from the July 5th, 2012 article titled "News Navigator: What is the record shogi player Yoshiharu Habu is close to breaking?" which probably can't be found online anymore. Here is another one from the Yomiuri Shimbun and its translation in The Japan News in an article titled "Behind the Scenes / Struggle for mastery in world of shogi," published on July 31st, 2018.

Yomiuri Shimbun:
東京都千代田区の都市センターホテルで１７日に行われた第８９期棋聖戦五番勝負第５局は、後年「将棋のタイトル戦の歴史上、一つの分岐点だった」といわれてもおかしくない勝負だった。

The Japan News:
It would not be surprising if this year's fifth and final match of the Kisei title series, which took place on July 17 at the Toshi Center Hotel in Chiyoda Ward, Tokyo, is one day considered a turning point in the history of shogi title matches.

I can't find links for any of the original articles, but I did find the article from The Japan News saved in an archive, so the reference links to that.