What is the phenotype ratio of this pentahybrid cross?

It depends on the dominance-recessive interaction. If all genes are complete dominance:
First split to single gene and then calculate all possibilities
Rr x Rr 3/4 R- : 1/4 rr
Ii x Ii 3/4 I- : 1/4 ii
Pp x Pp 3/4 P- : 1/4 pp
Aa x Aa 3/4 A- : 1/4 aa

So, the phenotypic ratio:
R-I-P-A- = 3/4 x 3/4 x 3/4 x 3/4 = 81/256
R-I-P-aa = 3/4 x 3/4 x 3/4 x 1/4 = 27/256
R-I-ppA- = 3/4 x 3/4 x 1/4 x 3/4 = 27/256
R-I-ppaa = 3/4 x 3/4 x 1/4 x 1/4 = 9/256
R-iiP-A- = 3/4 x 1/4 x 3/4 x 3/4 = 27/256
R-iiP-aa = 3/4 x 1/4 x 3/4 x 1/4 = 9/256
R-iippA- = 3/4 x 1/4 x 1/4 x 3/4 = 9/256
R-iippaa = 3/4 x 1/4 x 1/4 x 1/4 = 3/256
rrI-P-A- = 1/4 x 3/4 x 3/4 x 3/4 = 27/256
rrI-P-aa = 1/4 x 3/4 x 3/4 x 1/4 = 9/256
rrI-ppA- = 1/4 x 3/4 x 1/4 x 3/4 = 9/256
rrI-ppaa = 1/4 x 3/4 x 1/4 x 1/4 = 3/256
rriiP-A- = 1/4 x 1/4 x 3/4 x 3/4 = 9/256
rriiP-aa = 1/4 x 1/4 x 3/4 x 1/4 = 3/256
rriippA- = 1/4 x 1/4 x 1/4 x 3/4 = 3/256
rriippaa = 1/4 x 1/4 x 1/4 x 1/4 = 1/256
or 81 : 27 : 27 : 27 : 27 : 9 : 9 : 9 : 9 : 9 : 9 : 3 : 3 : 3 : 3 : 1