If you shoot from the same position with both lenses, then taking the 35mm lens and cropping it to the same angle of view of the 50mm lens will give you pretty much the same picture, other than the differences in optical quality between the two lenses and the resolution lost to cropping.

But even if you were to shoot with the same lens, shooting from a different distance will give a different perspective. This is because shooting distance is the only thing that determines perspective. The focal length and sensor size then determine the angle of view and framing from that shooting distance. So backing up with the 50mm lens to get the same framing of the subject as the 35mm would at a closer shooting distance also gives a different perspective: The relative sizes and shapes of items closer and further away from the camera will shift as the ratio of the distances of the various items to the camera changes.

Image copyright 2007 SharkD, licensed CC-BY-SA 3.0

Here's an extreme example of the effect differences in shooting distance have when using different focal lengths to get the same framing from different distances. The change in perspective is due to the change in shooting distance and the different distance ratios between the various elements in the scene and the camera as the camera moves forward and back to preserve framing of the subject at various focal lengths.

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A couple of explanations based on comments:

"will give you pretty much the same picture" -- What about the depth of field?

If you shoot from the same distance and use the same aperture with two different focal lengths you will have a difference in the depth of field. But by cropping the image from the wider angle lens you increase the magnification factor of the cropped image to view both images at the same display size. Remember, increasing the magnification also reduces the DoF.

Shooting at 15' with a 50mm lens on a FF camera at f/5.6 gives a DoF of 10.2': 3.5' in front of the focus distance and 6.6' behind (the rounding of each number gives the difference between the two components that total 10.1' and the 10.2' DoF). If you shoot from the same distance with the 35mm lens and crop it by a factor of 1.43X to give the same framing and use f/4 (f/3.92 to be precise) you have almost identical DoF, both in terms of total DoF and the front/back distribution.

Isn't the apparent distance between the foreground and background dependent on the focal length, even if you shoot from the same position and crop?

Nope. It is dependent upon shooting distance - both the distance from the camera to the subject/foreground and the distance from the camera to the background, and the ratio between the two. If you shoot from the same distance and crop perspective is identical.