A line and a circle intersect at $A$ and $B,$ as shown below. Find the distance between $A$ and $B$.

[asy]
usepackage("amsmath");
usepackage("amssymb");

unitsize(2 cm);

pair A, B;

A = dir(210);
B = dir(50);

draw(Circle((0,0),1));
draw(interp(A,B,-0.2)--interp(A,B,1.2));

dot("$A$", A, W);
dot("$B$", B, N);

label("$x^2 + y^2 = 5$", dir(135), NW);
label("$y = \dfrac{3x + 2}{4}$", interp(A,B,1.2), E);
[/asy]