Search results show in HTML5 help the name of the file as a clickable link not the title?

I think that text is based on the topic title in the Topic Properties dialog box. Have you checked that the Topic Title field is populated with the same text as your topic heading? I think that sometimes the file name can be populated in this field, possible if the content is imported.

Are you saying the blue text is not a link? Normally, it is a link to go to the found topic.

Did you make any changes to the layout? Any custom CSS that could be in the way?