I can recreate the spacing issue if Justify with last line aligned Left is selected as the paragraph style. Try applying Align left for the paragraph justification.
If you are exporting with Text Rendering set to either of the two HTML text options, then check if you have style overrides. You can view them by going to the Character Styles panel menu or the Paragraph Styles panel menu and selecting Toggle Style Override Highlighter. When that option is enabled, text that is formatted with overrides to the styles appear highlighted in cyan.
If you export with in5 and Text Rendering is set to Images, the style overrides shouldn't be an issue.
However, when you export with Text Rendering set to one of the HTML text options, in5 uses the Character, Paragraph, and Object Styles to create the CSS. If there are overrides, then in5 goes through a series of checks to try to "guess" what the style should be. These overrides can cause unintended results. So if you'd like to export with HTML text and the HTML text styles aren't rendering as expected, clear any style overrides.
Here's more information on Text Rendering:
If you're still having trouble with the text, would you be able to send us your InDesign file or a sample file that recreates the issue and your html5_output folder? You can send it to:
