+100

A chain that skips over the sprockets is NOT a RD issue. Putting a Dura-Ace RD on would not solve your problem. It is either a RD adjustment issue or (as everyone has said) the cogs on the freewheel are worn out. If it only skips in the smallest cog the high limit screw might be turned in too much.

If the RD shifts smoothly through all 5 cogs it is NOT to blame.