Hi John,
According to [http://www.ebay.com/itm/New-Toshiba-Satellite-L500-L505-L500D-L505D-LCD-Cable-6017B0198301-V000180110-US-/400397026449#vi-content|this here], a cable for a 15.6" screen seems to work in your case. And based on [http://www.ebay.com/itm/Genuine-New-Toshiba-Satellite-L500-L505-L505D-L500D-series-LCD-Cable-DC02000S800-/321151334625#vi-content|this website], it seems that the cable is only compatible with the S800 model. You might want to do some further research on that.
There are two versions of this cable, one for a LED screen, the other for a LCD version (see [http://any-pc-part.com/product_info.php/products_id/104134/405586|here]). I suppose you are looking for a LCD cable (P/N DC02000S800).
To avoid any risk and extra time, however, I would probably invest in [http://battery-adapter.com/product_info.php/products_id/4135/205586/vSatellite+L500+Series|this here], or [http://www.amazon.com/Brand-Video-Toshiba-Satellite-DC02000S800/dp/B008CTNA1W|here].
Steffen