5:1 AC Step Down Transformer

Wouldn't the resistance increase due to skin effect at higher frequencies..the conduction path is narrower because of skin effect.

No not at the frequencies we are talking about. Unless you are a self deluding Hi-Fi nut.

I just tested the resistance using an LCR meter.

thought resistance was a dc characteristic.

It is.

If the frequency does indeed effect intrinsic resistance, then the reading I got at 100 kHz of 60 ohms

There is the property of inductive reactant, perhaps your meter is measuring that, it is measured in ohms as well.