Port 135: MS RPC
Port 135 is the Windows RPC endpoint mapper, which tells other computers where Windows services are listening.
What runs on port 135
Windows uses Microsoft RPC for remote administration, DCOM, and many domain functions. The endpoint mapper on TCP 135 answers the question "which port is this service on" and points the client to a high dynamic port for the actual connection. Every Windows machine runs it.
On a home network
Every Windows PC listens on 135. The Windows firewall normally blocks it on networks marked public, but on a network marked private you may see it answer to a port scan. Macs, phones and routers do not use it.
If port 135 is reachable from the internet
Port 135 should never be reachable from the internet. In 2003 the Blaster worm spread by exploiting a flaw in Windows RPC over 135, infecting hundreds of thousands of PCs. It also leaks information about which services run on the machine, which helps attackers plan further steps.
How to check whether it is open on your network
A port scan of Windows PCs on your LAN will often show 135; that is normal inside. Make sure no router rule forwards it and that no PC is placed in the router's DMZ.
To find out whether port 135 is open on something in your home, and whether the internet can reach it, the app scans your Wi-Fi from your phone and checks your public address from the outside. It says what it checked and what it could not. Get RECON for iPhone — one-time purchase, no account, nothing leaves the device.