See code comments for answers.
clear variables
close all;
% dx must have 5 terms for n = 5
% the number terms in system equations
% must be the same as the number of
% elements in your dx vector.
% Remember your dot before *
dx = @(t,x) [x(1);x(1).*(2-x(1)-x(2));
x(2).*(3-x(1)-x(2)-x(3));
x(3).*(3-x(2)-x(3)-x(4));
x(4).*(3-x(3)-x(4)-x(5))];
tspan=[0 15];
x0=[0 2 0 3 0]; % same for the initial vector.
[t,x] = ode45(dx, tspan, x0);
figure(1)
plot(t, x);
