There are no online applications of which I am aware that work to give a shutter count for an EOS camera. This is mainly because the shutter count is not included in the EXIF information of images made using EOS cameras such as is the case with some cameras from some other manufacturers.

The shutter count from EOS cameras with DiG!C III and later processors up to cameras released by the end of 2014 make the shutter count available through the remote controlled interface that may be accessed on the camera via a USB connection. The remote control interface may also be accessed via WiFi connection for cameras so equipped with WiFi capability. This includes all DiG!C III, DiG!C 4, and DiG!C 5/5+ cameras. The EOS 7D Mark II is the only DiG!C 6/6+ camera that allows shutter count access via the remote controlled interface officially supported by Canon's SDK (software developers kit). None of the models released since early 2015 with DiG!C 6/6+ or later processors allow the shutter count to be accessed without the proprietary tools used by Canon service centers. For more detailed information about specific models, please see this page at dire studio's website.

Your EOS 5D Mark II falls into the group that allows the remote control application to access the camera's shutter count for still images taken with the camera. Live View actuations are not reported via the remote control interface. Only the Canon service centers can extract that info from EOS cameras.

The aforementioned Dire Studio offers an app called ShutterCount that works with compatible Canon EOS cameras listed above. Although it is not free, the cost is very modest. As of December 1, 2016 the Windows version is $3.99 USD and all other versions are $2.99 USD. I've been using it for about a year and a half and am very happy with it.

Update

Dire Studio has released ShutterCount version 3 (currently for Mac or iOS only) that can now read the shutter counts for the cameras excluded above, as well as some other more recent models. From the updated FAQ page as of July 2, 2017:

Q13 - The shutter count is not displayed for new cameras (5D IV, 5DS/R, 1D X II, etc.)

Update to ShutterCount 3.0 or later on your Mac or iOS device. The Windows version will support these cameras later on.

Dire Studio also now offers an add-on Live View Pack to their Shutter Count app that allows one to see Live View stills and Live View movie actuations of the shutters in selected cameras.

Unfortunately, it doesn't look like Dire Studio is interested in ever updating the Windows version again, due to the high cost of Microsoft licensing. They once had a statement to this effect included in one of the FAQs, but it seems to no longer be there at their site.

For a list of all supported cameras, please see the Compatibility List at the ShutterCount Tech Specs page.

As of 22 February, 2018 there has still been no update to the Windows version of Shutter Count. In fact, the older version compatible with Windows is no longer offered for sale by Dire Studio.

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Prior to buying ShutterCount I was using a free app called EOSInfo. However, there are some security concerns floating around the internet about that program's developer so I chose to stop using it.

You can also access the internal shutter count on certain EOS cameras using Magic Lantern. To use Magic Lantern to access the shutter count you must have one of the cameras for which there is also a version of Magic Lantern available. The original version of magic Lantern was developed for the EOS 5D Mark II and is perhaps the most stable version of ML there is. Since ML is third party software there is some risk in using it.