The Slingbox 500 with quality settings set to Best HD will display in resolution 640X240, 640X480, 1280X720, 1280X544, 1440X544, 1680X544, 1920X544. There is away to select what Streaming resolution that will displayed to SlingPlayer app. I have listed below an article to help you adjust to highest resolution.
Sling Media Moderation Team
Unfortunately there is no "Slingplayer Options" entry in the Settings menu in the Slingplayer IOS app.
I then tried web browser access to my Slingbox settings, but I couldn't find any video streaming quality settings there either (other than "auto" or "sd").
In that article, under Affected Products, it says Slingplayer for Windows (legacy), so I guess the article doesn't apply to the IOS app or web browser access. Is there anywhere else I can check?