http.Server allows us to pass a context for the shutdown operation. This allows to us to use some of the context capabilities, such as cancelling and timeout. We can define a new server with its mux and a cancellable context:

mux := http.NewServeMux()
server := http.Server{
    Addr: ":3000",
    Handler: mux,
}
ctx, canc := context.WithCancel(context.Background())
defer canc()
mux.HandleFunc("/shutdown", func(w http.ResponseWriter, r *http.Request) {
    w.Write([]byte("OK"))
    canc()
})

We can launch the server in a separate goroutine:

go func() {
    if err := server.ListenAndServe(); err != nil {
        if err != http.ErrServerClosed {
            log.Fatal(err)
        }
    }
}()

The context will be complete when the shutdown endpoint is called and the cancellation function is invoked. We can wait for that event and then use another context with a timeout to call the shutdown method:

select {
case <-ctx.Done():
    ctx, canc := context.WithTimeout(context.Background(), time.Second*5)
    defer canc()
    if err := server.Shutdown(ctx); err != nil {
        log.Fatalln("Shutdown:", err)
    } else {
        log.Println("Shutdown:", "ok")
    }
}

This will allow us to terminate the server effectively within the timeout, after which it will terminate with an error.