STAIR

HONED

CLUMP

MOUNT

I tried out the first 3 words suggested by @Mother as containing the most common letters in the dictionary in descending order and they worked beautifully. I almost got it at 3 but decided to type in clump anyway to fully test them out rather than having a long think after honed, if I had I think there was a chance I'd have gotten it but as it is I'm still very happy with 4/6.