This may be true about the times with numbers divisible by 5 not having 'minutes' when being read.
However, I find there are many, many ways to deliver the time, especially by radio announcers. I think they try to find new, different and 'interesting' ways to say the time.
First, we all use the digital time: two-thirty-two, one-oh-four, eleven-fifteen, etc.
Then, I have heard all kinds of fanciness, something like these:
It's twenty-four minutes to one.
It's twenty-four minutes before one.
It's fifteen past three.
It's fifteen minutes after three.
and many more!
Let's pay attention and add some of these creative time-telling phrases to this thread.