"There is 1 unread and 4 new topics remaining, or browse other topics in ..."

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This is the sort of restructuring I had in mind, to turn it into a proper sentence.

Going back to the text I didn’t like, it would become:

See 1 unread topic and 4 new topics, or browse other topics in…

Or, to reduce repetition:

See 1 unread topic and 4 new topics, or browse…