Out of 3 wands purchased, Kate sold her friends 3 wands - 1 wand = <<3-1=2>>2 wands.
For 2 wands she charged $130, so for 1 wand she charged $130 / 2 wands = $<<130/2=65>>65/wand.
Since she charged $5 more for each wand than she paid, Kate paid $65 - $5 = $<<65-5=60>>60 for each wand.
#### 60