Catalyzes preferentially the transfer of L-fucose, from a guanosine diphosphate-beta-L-fucose, to the N-acetyl-beta-D-glucosamine (GlcNAc) of an N-acetyllactosamine unit (type 2 chain) of an oligosaccharide, or a glycoprotein- and a glycolipid-linked N- acetyllactosamine unit via an alpha (1,3) linkage and participates in the surface expression of VIM-2, Lewis X/SSEA-1 and sialyl Lewis X antigens (PubMed:14718375, PubMed:1740457, PubMed:17604274, PubMed:29593094, PubMed:7721776, PubMed:9737988, PubMed:9737989). Preferentially transfers fucose to the GlcNAc of an internal N- acetyllactosamine unit of a poly-N-acetyllactosamine chain acceptor substrate (PubMed:17604274, PubMed:7721776). Also catalyzes to a lesser extend the transfer of L-fucose to the GlcNAc of a type 1 (beta-D- galactosyl-(1->3)-N-acetyl-beta-D-glucosaminyl) or H-type 1 (alpha-L- Fuc-(1->2)-beta-D-Gal-(1->3)-D-GlcNAc) chain oligosaccharide via an alpha (1,4) linkage (PubMed:14718375, PubMed:1740457, PubMed:17604274, PubMed:7721776, PubMed:9737988). Preferentially catalyzes sialylated type 2 oligosaccharide acceptors over neutral type 2 or H type 2 (alpha-L-Fuc-(1->2)-beta-D-Gal-(1->4)-D-GlcNAc) oligosaccharide acceptors (PubMed:1740457, PubMed:9737989). Lactose-based structures are also acceptor substrates (PubMed:1740457, PubMed:7721776). {ECO:0000269|PubMed:14718375, ECO:0000269|PubMed:1740457, ECO:0000269|PubMed:17604274, ECO:0000269|PubMed:7721776, ECO:0000269|PubMed:9737988, ECO:0000269|PubMed:9737989}. This is the function of FUT5 (fucosyltransferase 5, Ensembl gene identifier ENSG00000130383).