The archives go back several months and 5 minutes seemed to be the approximate length of the texts when read.
Though I came away empty handed from the BBC's Russian and Chinese services. a bit of poking around revealed that some matching text and audio is available from Voice of America-Chinese* (voachinese.com) and Radio Free Europe-Russian* (svoboda.org), as well as Radio Canada International-Chinese (http://www.rcinet.ca/zh/category/a-l-affiche/em...). While I had an easier time finding items with matching text and audio on the RFI sites than the others, even at RFI it took a good deal of exploration to hit upon those materials meeting the LingQ ideal.
(*To the best of my knowledge, both are still under the auspices of the USA's Broadcasting Board of Governors.)
I've just discovered that the Freakonomics podcasts have transcripts. These would be suitable for advanced English students. My husband listens to them a lot and recommends them highly: http://www.freakonomics.com/tag/freakonomics-po...