Docker + Nginx + PHPで実際にメールを送信したい

実現したいこと

Docker + Nginx + PHPで実際にメールを送信したい
mailhogだと実際にメールが送信されないので、どのように実装すればいいかわかっていません

発生している問題・エラーメッセージ

gmailやicloudにメールが送信されない。

php
1if(mb_send_mail("test@gmail.com", "test_sub", "test_body", "test_header")){
2     echo "成功";
3} else {
4     echo "失敗";
5}

「成功」が出力されるのですが、メール受信ができません

ご教示いただけますと幸いです

ファイル構成

/test
└ docker-compose.yml
    ├ nginx
    │  ├ Dockerfile
    │  ├ default.conf
    │  └ nginx.conf
    └ app
        ├ index.php
        ├ Dockerfile
        ├ php.ini
        ├ sendmail.ini
        └ update-exim4.conf

該当のソースコード

docker
1version: "3"
2services:
3  nginx:
4    build:
5      context: ./nginx
6    ports:
7      - 8080:8080
8    volumes:
9      - ./app:/usr/share/nginx/html
10
11  php:
12    image: php:7-fpm
13    build:
14      context: ./app
15    ports:
16      - 25:25
17    volumes:
18      - ./app:/usr/share/nginx/html
19

app/Dockerfile
1FROM php:7-fpm
2COPY php.ini  /usr/local/etc/php/php.ini
3COPY sendmail.ini /usr/local/etc/php/conf.d/
4COPY update-exim4.conf /etc/exim4/update-exim4.conf.conf
5RUN apt-get -y update && apt-get install -y msmtp mailutils

app/index.php
1<?php
2    mb_language("Japanese");
3    mb_internal_encoding("UTF-8");
4
5    $to = 'xxxxxx@example.com';
6    $subject = "テスト";
7    $body = "これはテストです。\n";
8    $from = "xxxxxx@example.com";
9    $header = "From: $from\nReply-To: $from\n";
10
11   mb_send_mail($to, $subject, $body, $header);
12?>

app/php.ini
1[Date]
2date.timezone = "Asia/Tokyo"
3
4[mbstring]
5mbstring.language = Japanese
6mbstring.internal_encoding = UTF-8

app/sendmail.ini
1sendmail_path = /usr/sbin/sendmail -t

app/update
1dc_eximconfig_configtype='internet'
2dc_other_hostnames=''
3dc_local_interfaces='127.0.0.1;::1'
4dc_readhost='exim4'
5dc_relay_domains=''
6dc_minimaldns='true'
7dc_relay_nets=''
8dc_smarthost=''
9CFILEMODE='644'
10dc_use_split_config='true'
11dc_hide_mailname='true'
12dc_mailname_in_oh='true'
13dc_localdelivery='mail_spool'

nginx/default.conf
1server {
2    listen       8080;
3    listen  [::]:8080;
4    server_name  localhost;
5
6	root   /usr/share/nginx/html;
7	index  index.html index.htm index.php;
8
9    location / {
10    	try_files $uri $uri/ /index.php$is_args$args;
11    }
12    
13    error_page   500 502 503 504  /50x.html;
14    location = /50x.html {
15        root   /usr/share/nginx/html;
16    }
17
18    location ~ \.php$ {
19        root           /usr/share/nginx/html;
20        fastcgi_pass   php:9000;
21        fastcgi_index  index.php;
22        fastcgi_param  SCRIPT_FILENAME  $document_root$fastcgi_script_name;
23        include        fastcgi_params;
24    }
25
26}
27

nginx/Dockerfile
1FROM nginx:latest
2
3COPY default.conf /etc/nginx/conf.d
4COPY nginx.conf /etc/nginx/nginx.conf

nginx/nginx.conf
1user  nginx;
2worker_processes  auto;
3
4error_log  /var/log/nginx/error.log notice;
5pid        /var/run/nginx.pid;
6
7events {
8    worker_connections  1024;
9}
10
11http {
12    include       /etc/nginx/mime.types;
13    default_type  application/octet-stream;
14
15    log_format  main  '$remote_addr - $remote_user [$time_local] "$request" '
16                      '$status $body_bytes_sent "$http_referer" '
17                      '"$http_user_agent" "$http_x_forwarded_for"';
18
19    access_log  /var/log/nginx/access.log  main;
20    sendfile        on;
21    keepalive_timeout  65;
22    include /etc/nginx/conf.d/*.conf;
23}
24