Depending on the answer to my comment, this is a first attemptWith tab-separated files:
awk '
BEGIN { FS = OFS = "\t" }
NR == FNR {fn[$1] = $4 "_" $5;$4; next}
{fprint =$1, $2, $3, ($3 in fn) ? fn[$3] : "FALSE"; print $1, $2, $3, f"FALSE"), $4, $5}
' file2.txt file1.txt | column -t
Query No. Accession Function_ Function Name DB
EFX03602.1 1006 PHI:1006 HMG-CoA_ReductaseCoA Reductase HMR1 Not_Available
EFX00827.1 101 PHI:101 Polyketide_synthasePolyketide synthase ALB1 AAC39471
EFX01509.1 101 PHI:101 Polyketide_synthasePolyketide synthase ALB1 AAC39471
EFX05810.1 1010 PHI:1010 FALSE FALSE SID1 XM_385547
EFX00466.1 1026 PHI:1026 Phospholipase_C Phospholipase C bcplc1 AAB39564