This can do the trick:

$ perl -lane '($n,$d)=split(/\//,$F[4]); $F[4]=$n/$d; print join "\t", @F' < table.txt
A       B       2.9711e-01      6.8662e-10      0.0009765625
A       C       2.3343e-03      0.0000e+00      0.90869140625
A       D       2.9711e-01      6.8666e-10      0.0009765625
A       E       2.9711e-01      6.8658e-10      0.0009765625

You can try awk, too, assuming that your file's format is consistent (no empty cells; tab-delimited) and that there is indeed no header:

awk -F "\t" '{
  split($5, div, "/");
  print $1"\t"$2"\t"$3"\t"$4"\t"div[1]/div[2]}' table.txt

A   B   2.9711e-01  6.8662e-10  0.000976562
A   C   2.3343e-03  0.0000e+00  0.908691
A   D   2.9711e-01  6.8666e-10  0.000976562
A   E   2.9711e-01  6.8658e-10  0.000976562

Kevin

$ awk '{split($5, v, "/"); OFS="\t"; print $1,$2,$3,v[1]/v[2]}' foo.txt
A       B       2.9711e-01      0.000976562
A       C       2.3343e-03      0.908691
A       D       2.9711e-01      0.000976562
A       E       2.9711e-01      0.000976562

Just to keep the tradition of questions with no clear relation to bioinformatics attracting lots of answers (and because it is Friday night at times of pandemics), here are some alternative solutions:

Using several bash variables:

while IFS=$'\t' read -r val1 val2 val3 val4 val5
do
    val5=$(echo "scale=10; $val5" | bc -l)
    printf "%s\t%s\t%s\t%s\t%s\n" "$val1" "$val2" "$val3" "$val4" "$val5"
done < table.tsv

With an array, slicing the array to delete the last element and replace by the result of the division:

while IFS=$'\t' read -r -a array
do
    val=$(echo "scale=10; ${array[-1]}" | bc -l)
    array=("${array[@]::${#array[@]}-1}")
    array+=($val)
    printf "%s\t" "${array[@]}"; echo
done < table.tsv

For modern (later than 4.2, I think) bash, one can use a nicer syntax to delete the last array element:

while IFS=$'\t' read -r -a array
do
    val=$(echo "scale=10; ${array[-1]}" | bc -l)
    unset array[-1]
    printf "%s\t" "${array[@]}"
    printf "%s\n" "$val"
done < table.tsv