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Edit: Note to self, don't post before you're actually awake enough to read the OP

This is usually an aspect ratio problem. Either your graphics card program or DOSBox's config tells it to show the original resolution instead of stretching the image.

I can't seem to figure out how to fix this problem. I go into the GOG Galaxy folder, click King's Quest 5's Dosbox Configurator and it shows the option to Keep Aspect Ratio, change the resolution and Full Screen. But doesn't seem to change anything when I open the game. What am I doing wrong?

Check your graphics card options (nvidia control panel) and make sure you have scaling set to "full screen" instead of "no scaling." Maybe?

Didn't fix the problem, I think it's a problem with DOSBox, but I'm not to savey with DOSBox. Anyone know how to mess with the settings on DOSBox in order to effect all my games?

This happens when you start a game? For me what happens is I get fullscreen mode with dosbox BUT, if I tab out, then it goes small and won't go back unless I close+reopen the game. I've never had to mess with dosbox options. I would suggest contacting support. Though hopefully someone here might be able to help.

yea it happens every time I start a game that runs on DOSBox. The game will start in Full Screen Mode, but you'll only see the game at the center of the screen, with black borders. If I alt - tab out and click the game it then goes into Window Mode, so I no longer have a problem in that sense, but it's still small so I'd just like to know how to make it so the game fits the entire screen while in Full Screen mode.

I'm at a loss, good luck!

You could try going into the directory of the game and finding the .conf file.
Find the line that says "fullresolution=" and change that to "fullresolution=0x0".

Gpu playing with aspect ratio and scaling? Seems like that.
Check your Nvidia Control Panel/Catalyst Control Center/Intel GPU options

But just in case:
Check the games install folder and change the files in the games dosbox conf to your desired values.

Usually name is gamename_dosbox.conf (usually) and it's located in the game's folder. Open with notepad of your choice
(Notepad++ master race)

Check values with if not certain:
http://www.dosbox.com/wiki/Dosbox.conf#Sections

Change resolution, the old dos games had low resolutions which seem very tiny on newer higher resolution displays. (Have you tried 640x480 on 4K monitor with native resolution :D)

If you are talking about GOG (DOSbox) games, each game uses their own DOSBox, so you need to edit the dosbox conf file for each GOG game individually, which have this problem.

Can you open the dosbox conf file for some GOG game that has this problem (with WordPad, if it is unreadable with Notepad due to not having linefeeds), and present here what settings you have under [sdl] and [render]? Then we are able to give suggestions.

To find the dosbox config file, you have to go to the directory where the game is installed (not the Start Menu links). For instance for my M.A.X. GOG game, the related DOSBox config file is here (the default place where it is installed):

C:\GOG Games\MAX\dosboxMAX1.conf

If you installed the game with Galaxy, not sure where it installs the games by default.

Do you mean the game is running at 4:3 fullscreen with black borders on the sides? Or is the issue something else, like the game running in a small square in the middle of the screen surrounded by black borders on all sides?

If it's the latter, try changing the graphic mode. The default is 'surface'.

Also, what is your operating system?

It's what you said, where the game is running in a small square in the middle of the screen surrounded by black borders on all sides. I tried your tip to change the Graphic Mode to all the different ones that were listed, and it didn't fix the problem. I am using Windows 10.

Like me, it sound like you are playing on a TV or other display that doesn't have hardware scaling. In your video card control panel, set scaling to GPU. This should generally resolve issues that are related to device scaling. If not, you can force each one manually by editing the dosbox.conf file so that aspect=true, output= (anything besides surface, e.g. ddraw), and resolution = your displays maximum res.