Completing Gray Code Given Initial Part
This is one way of doing it logically. Convert the gray code to binary code so you get to linear space. Add one, or some other number, then go back to gray code and insert it into the table. 



Converting gray code to binary code can be done according to these boolean equations: 

\$
B_4 = G_4 \\
B_3 = B_4\oplus G_3\\
B_2 = B_3\oplus G_2\\
B_1 = B_2\oplus G_1\\
B_0 = B_1\oplus G_0
\$

So let's do this for the last one you have so we can get to binary code.

\$
B_4 = 1 \\
B_3 = 1\oplus 1 = 0\\
B_2 = 0\oplus 1 = 1\\
B_1 = 1\oplus 1 = 0\\
B_0 = 0\oplus 1 = 1
\$

So the binary value is \$10101_2\$, which is \$21_{10}\$ in ordinary decimal. Let's increment it by 1 so we can get to our next gray code value. Adding one gives us \$10110_2=22_{10}\$. What we have here could be useful for incrementing the value again by 1 so we can get the next consecutive gray code. Or we could identify the white rows in the table with this information, and calculate the gray code with that information. 

Converting binary code to gray code can be done according to these boolean equations:

\$
G_4 = B_4\\
G_3 = B_4 \oplus B_3\\
G_2 = B_3 \oplus B_2\\
G_1 = B_2 \oplus B_1\\
G_0 = B_1 \oplus B_0
\$

So let's do this for the last one you have so we can get to binary code.

\$
G_4 = 1\\
G_3 = 1 \oplus 0 = 1\\
G_2 = 0 \oplus 1 = 1\\
G_1 = 1 \oplus 1 = 0\\
G_0 = 1 \oplus 0 = 1
\$

So the next gray code is \$11101_2\$. The white space that I assume you are supposed to fill in are the numbers 26 to 29 in binary, meaning the gray code I've calculated won't help you. So I will leave the actual part of the homework to you.



Though I believe the easiest thing to do, realistically for you as a human, would be to simply make the 5 bit gray code table and identify the positions of the missing entries and fill them in accordingly. 

Or another thing that is also easy to do is to just simply learn the pattern. The leftmost column is a copy of the binary system. The second to leftmost column is the same as leftmost binary column just half way up. The third to leftmost column is the same as second to leftmost binary column just 1/4th way moved up. And I presume you can see the pattern by now.