I'll add my answer as @Maxime's answer works, but there is actually no need for a subject.

This is done using the .concat() operator and recursion with the getData() function.

.concat()

Concatenates multiple Observables together by sequentially emitting their values, one Observable after the other.

(...)

concat will subscribe to first input Observable and emit all its values, without changing or affecting them in any way. When that Observable completes, it will subscribe to then next Observable passed and, again, emit its values. This will be repeated, until the operator runs out of Observables. When last input Observable completes, concat will complete as well.

(I used the js version in order to make a snippet that works with stack Overflow's tool, but this is the same for typescript):

function someHTTPCall() {
  // well it's a fake http call
  console.log("making the Http request (can take up to 5s)...");
  return Rx.Observable.of("http response !")
    .delay(Math.round(Math.random() * 5000));
}

function getData() {
  return someHTTPCall()
    .concat(Rx.Observable.timer(5000).switchMap(() => getData()));
}

let myObs = getData();

myObs.subscribe((data) => {
  console.log(data,"waiting for 5 seconds before next request");
});

<script src="https://unpkg.com/rxjs@5.4.0/bundles/Rx.min.js"></script>

This is an interesting question and I had some fun to come up with a solution.

This solution wait for the previous to finish as you expect :

const { Observable, Subject } = Rx

const getFakeHttpRequest$ = () => Observable.of('response !').delay(3000)

const polling$ = new Subject()

Observable
  // need to tick the first time
  .of(null)
  // everytime our polling$ subject will emit, we'll do again what's next
  .merge(polling$)
  // register to a fake request
  .switchMap(_ =>
    getFakeHttpRequest$()
      .do(_ => {
        // once we're here, the request is done
        // no mater how long it was to get a response ...
        console.log('HTTP request done !');

        // ... we wait 5s and then send a new value to polling$ subject
        // in order to trigger a new request
        setTimeout(_ => polling$.next(null), 5000)
      })
  )
  .subscribe()

Notice that I've put a 3s delay on the request, and that a new request kicks in every 8s, as we waited 3s for the response and then 5s as requested in your question.

Here's a working Plunkr : https://plnkr.co/edit/kXefUbPleqyyUOlfwGuO?p=info

you can use the interval operator:

private poller(): Observable<PrepareData> {
    return Observable.interval(5000).switchMap(() => this.http.get("/cgi/dashboard.php")).map(res => res.json());
}