The latest episodes of TLC shows are not available through any approved sites. There are lots of sites out there where fans might post portions of shows, or illegal sites that post and host full episodes. However, Wiki.answers doesn't endorse doing anything illegal, so your best bet is to check out the webisodes on the official site.
If you go to TLC's website they have some up, and you can also try YouTube. They have alot of episodes posted by users.
http://tlc.com/
http://youtube.com/
A few episodes are available from the TLC's website, also full episodes are available via iTunes for a fee.
There is no season five of 19 kids and counting, they just finished the first season, so, no, you can't watch it online, in fact, you can't want it anywhere, because it hasn't happened yet.
youtube.
17 Kids and Counting - 2008 Duggars Act Out - 6.5 was released on: USA: 7 February 2011
17 Kids and Counting - 2008 Kids to the Rescue 7-2 was released on: USA: 14 June 2011
17 Kids and Counting - 2008 A Duggar on Her Own was released on: USA: 25 September 2012
17 Kids and Counting - 2008 Designing Duggars - 3.27 was released on: USA: 15 December 2009
17 Kids and Counting - 2008 2012-10-30 was released on: USA: 30 October 2012
in 18 kids and counting episode duggars on ice and duggars big thaw watch both
17 Kids and Counting - 2008 38 Kids and Counting 8-7 was released on: USA: 18 October 2011
17 Kids and Counting - 2008 is rated/received certificates of: Australia:PG
17 Kids and Counting - 2008 was released on: USA: 29 September 2008
17 Kids and Counting - 2008 Duggars Act Out - 6.5 was released on: USA: 7 February 2011
17 Kids and Counting - 2008 Kids to the Rescue 7-2 was released on: USA: 14 June 2011
17 Kids and Counting - 2008 Royal Duggars was released on: USA: November 2011
17 Kids and Counting - 2008 Duggars at the Hospital 4-17 was released on: USA: 11 May 2010
17 Kids and Counting - 2008 First GrandDuggar 3-17 was released on: USA: 13 October 2009
17 Kids and Counting - 2008 Engaging Announcement was released on: USA: 15 October 2013
17 Kids and Counting - 2008 Planning the Future was released on: USA: 14 February 2012
17 Kids and Counting - 2008 Anniversaries to Remember was released on: USA: 8 October 2013