Take a common denominator of $60$ for the two given fractions: $3/4 = 45/60$, $5/6 = 50/60$.
Check the options on the same denominator: $4/5 = 48/60$, $3/5 = 36/60$, $7/5 = 84/60$, $6/5 = 72/60$.
Only $48/60$ lies strictly between $45/60$ and $50/60$.
\[\boxed{4/5}\]