Scanf parsing string input into array of chars

You haven't allocated memory for your strings. The arguments you give to scanf are uninitialized pointers.

top[i] = "test" assigns a pointer to your variable and initializes it with a valid value.

In contrast, scanf(..., top[i]) tries to write to where top[i] points. But top[i] isn't initialized and points to some random location, which results in your memory access error.

When you look at man scanf, you can read under

Conversions
...
s
Matches a sequence of non-white-space characters;

and now the important part

the next pointer must be a pointer to character array that is long enough to hold the input sequence and the terminating null byte ('\0'), which is added automatically.

So you must allocate an array via malloc() or declare the character array large enough.

char top[10][21];
char bottom[10][21];
int i;
for(i = 0; i < 5; i++){
    printf("Karte %d: Obere Werte? ", i);
    scanf("%20s",top[i]);
    printf("Karte %d: Untere Werte? ", i);
    scanf("%20s",bottom[i]);
}

With

scanf("%20s",top[i]);

you limit the number of characters read, to prevent a buffer overrun

As another answer says, you have to allocate place for your strings. You want an array of top and bottom strings, but with char * top[10] you are only allocating room for 10 pointers, not for the characters in the strings. The reason why top[10] = "Hello" works is that string literals are implicitly allocated by the compiler, which returns a pointer to those characters.

char *top[10], *bottom[10];
for(i = 0; i < 5; i++)
{
    top[i] = malloc(100); // reserve room for string up to 100 chars
    printf("Karte %d: Obere Werte? ", i);
    scanf("%s",top[i]);
    bottom[i] = malloc(100);
    printf("Karte %d: Untere Werte? ", i);
    scanf("%s",bottom[i]);
}

What you have is an array of pointers. You need to allocate memory for each pointer in array.

You can do the following before scanf.

top[i] = malloc(sizeof(char)*255);
bottom[i] = malloc(sizeof(char)*255);

After use don't forget to free.

free(top[i]);
free(bottom([i]);