Estoy tratando de implementar una conexión TCP, todo funciona bien desde el lado del servidor, pero cuando ejecuto el programa cliente (desde la computadora cliente) aparece el siguiente error:

java.net.ConnectException: Connection refused
        at java.net.PlainSocketImpl.socketConnect(Native Method)
        at java.net.PlainSocketImpl.doConnect(PlainSocketImpl.java:351)
        at java.net.PlainSocketImpl.connectToAddress(PlainSocketImpl.java:213)
        at java.net.PlainSocketImpl.connect(PlainSocketImpl.java:200)
        at java.net.SocksSocketImpl.connect(SocksSocketImpl.java:432)
        at java.net.Socket.connect(Socket.java:529)
        at java.net.Socket.connect(Socket.java:478)
        at java.net.Socket.<init>(Socket.java:375)
        at java.net.Socket.<init>(Socket.java:189)
        at TCPClient.main(TCPClient.java:13)

ntenté cambiar el número de socket en caso de que estuviera en uso, pero fue en vano, ¿alguien sabe qué está causando este error y cómo solucionarlo?

El código del servidor:

//TCPServer.java

import java.io.*;
import java.net.*;

class TCPServer {
    public static void main(String argv[]) throws Exception {
        String fromclient;
        String toclient;

        ServerSocket Server = new ServerSocket(5000);

        System.out.println("TCPServer Waiting for client on port 5000");

        while (true) {
            Socket connected = Server.accept();
            System.out.println(" THE CLIENT" + " " + connected.getInetAddress()
                    + ":" + connected.getPort() + " IS CONNECTED ");

            BufferedReader inFromUser = new BufferedReader(
                    new InputStreamReader(System.in));

            BufferedReader inFromClient = new BufferedReader(
                    new InputStreamReader(connected.getInputStream()));

            PrintWriter outToClient = new PrintWriter(
                    connected.getOutputStream(), true);

            while (true) {

                System.out.println("SEND(Type Q or q to Quit):");
                toclient = inFromUser.readLine();

                if (toclient.equals("q") || toclient.equals("Q")) {
                    outToClient.println(toclient);
                    connected.close();
                    break;
                } else {
                    outToClient.println(toclient);
                }

                fromclient = inFromClient.readLine();

                if (fromclient.equals("q") || fromclient.equals("Q")) {
                    connected.close();
                    break;
                } else {
                    System.out.println("RECIEVED:" + fromclient);
                }

            }

        }
    }
}

El Código del Cliente:

//TCPClient.java

import java.io.*;
import java.net.*;

class TCPClient {
    public static void main(String argv[]) throws Exception {
        String FromServer;
        String ToServer;

        Socket clientSocket = new Socket("localhost", 5000);

        BufferedReader inFromUser = new BufferedReader(new InputStreamReader(
                System.in));

        PrintWriter outToServer = new PrintWriter(
                clientSocket.getOutputStream(), true);

        BufferedReader inFromServer = new BufferedReader(new InputStreamReader(
                clientSocket.getInputStream()));

        while (true) {

            FromServer = inFromServer.readLine();

            if (FromServer.equals("q") || FromServer.equals("Q")) {
                clientSocket.close();
                break;
            } else {
                System.out.println("RECIEVED:" + FromServer);
                System.out.println("SEND(Type Q or q to Quit):");

                ToServer = inFromUser.readLine();

                if (ToServer.equals("Q") || ToServer.equals("q")) {
                    outToServer.println(ToServer);
                    clientSocket.close();
                    break;
                } else {
                    outToServer.println(ToServer);
                }
            }
        }
    }
}