Is the last update is 5.5.2 ?
Yes it the latest fw, and most likely the last update for Wii U.
However, i wouldn't recommend updating to it without Haxchi. Since the exploit for it fails a lot.
If you really don't want Haxchi (for whatever reason)
like i said, you can buy Color Splash and let it update to 5.5.1, which has a more stable browser exploit.
However you'd waste more money on that than getting a DS game on the e-shop for haxchi.