From
this image (which I presume to be an E1705), you don't have an HDMI port, but you do have a DVI port, which you should be able to use to connect your laptop to your monitor.
From
this image, it seems like Fn+F8 is the key combination you have to put when you want to sync your computer with your monitor after you connect the cord (make sure the monitor is also outputting on the signal you want it to display in).
Even with a VGA plug, I've been able to output my laptop onto my 20" WSXGA+ Dell E207WFP monitor. However, when I tried to output the same laptop onto a Samsung DLP HDTV, I had issues with resolution (I don't think the cord was the bottleneck, I was thinking it was some setting in the TV).