You can't do that through the any dashboard settings. Yould would need to override the block edit dialog or the block controller (or both).

For example, you could add a validation method to an override of the block controller that would return an error object if the length of a text entry was greater than a limit.

Or you could create a modified edit dialog that simply refused to accept any excess input.

For a core content block, the controller validate is probably simplest to set up.

You would also need to decide on whether to count the absolute length (including any embedded tags), or the text length (plain text,without tags).

Boy, this sounds complicated. I thought content management was really all about content control. Is this the only way designers ensure that Concrete5 pages don't become a complete mess once users start editing them??

I did find a plugin for the redactor editor.
http://imperavi.com/redactor/plugins/limiter/...

But I didn't test it, nor installed it on concrete5

This plugin seems to do the job the OP is asking for (by using the example on the URL). By default this is not a feature that comes with Concrete5 (unfortunately).