Reduce from two pure functions to one

Question

Liking the headings and spacing allowed by Row[] and TableForm[] I set up the below with 3 TableForm[]'s to use as a model from which to generalize, using a pure function, to display a list of 3-ples, coEffs10.
The lower Row[...], is the general one, using one TableForm[], and provides correct output, but uses 2 pure functions - I couldn't do it in 1.

1. I'm curious to see the same output produced with Row[TableForm[...]] but using only a single pure function.
2. Also, keeping the pair of pf's, but disentangling them to the point that they could both be put in " |-> " form, which I was unable to do.

I suspect the answers are implicit in 38393, but are too subtle for me.

Thanks.

coEffs10={{1,2,0},{2,3,0},{3,5,1},{4,7,5},{5,11,3},{6,13,0},{7,17,7},{8,19,10},{9,23,3},
          {10,29,3},{11,31,30},{12,37,25},{13,41,18},{14,43,16},{15,47,19}};

tH = {None, {"n", "p[n]", "cof"}};
Row[{
     TableForm[coEffs10[[1 + 0*5 ;; (0+1)*5]] , TableAlignments -> Right, TableSpacing -> {1,2}, TableHeadings -> tH],
     TableForm[coEffs10[[1 + 1*5 ;; (1+1)*5]] , TableAlignments -> Right, TableSpacing -> {1,2}, TableHeadings -> tH],
     TableForm[coEffs10[[1 + 2*5 ;; (2+1)*5]] , TableAlignments -> Right, TableSpacing -> {1,2}, TableHeadings -> tH]
     },
     Spacer[43]
     ]

The below generalizes above, but uses 2 pure functions. Can it be done with one?

Row[
    TableForm[coEffs10[[1 + (#1-1) 5 ;; #1 5]]&[#],
       TableAlignments -> Right, TableSpacing -> {1,2}, TableHeadings -> tH]& /@ Range[3],
    Spacer[43]
   ]  

Answer 1

Row[TableForm[coEffs10[[1 + (# - 1) 5 ;; # 5]] , 
    TableAlignments -> Right, TableSpacing -> {1, 2}, 
    TableHeadings -> tH] & /@ Range[3], Spacer[43]]