The problem asks us to count the number of complex numbers that lie in or on the circle of radius 5 centered at the origin, with integer real and imaginary parts.

[asy]
unitsize(0.5 cm);

int i, j;

draw((-5,0)--(5,0));
draw((0,-5)--(0,5));
draw(Circle((0,0),5));

for (i = -5; i <= 5; ++i) {
for (j = -5; j <= 5; ++j) {
  if (i^2 + j^2 > 25) {dot((i,j));}
  if (i^2 + j^2 <= 25) {dot((i,j),red);}
}}
[/asy]

We can count that there are 15 such complex numbers in the first quadrant (not including the axes).  Then there are 5 complex on the positive real axis, the negative real axis, the positive imaginary axis, and negative imaginary axis.  Finally, there is the origin itself, which gives us $4 \cdot 15 + 4 \cdot 5 + 1 = \boxed{81}$ complex numbers.
Question:
Find the number of ordered pairs $(a,b)$ of integers such that $|a + bi| \le 5.$
Answer:
Let's think step by step.

user
81
Find the number of ordered pairs $(a,b)$ of integers such that $|a + bi| \le 5.$
test