Looking to understand the difference between (Fibroblast Growth Factor) FGF-2 and FGF-5
I'd suggest looking at this article on the FGF family. You will find a lot of information there about comparative analysis of the different proteins therein. For example (FGFR = FGF receptor, which binds FGF to transmit signals):

FGF–FGFR binding specificity is regulated both by primary sequence differences between the 18 FGFs and the 7 main FGFRs (FGFR1b, FGFR1c, FGFR2b, FGFR2c, FGFR3b, FGFR3c and FGFR4) and by temporal and spatial expression patterns of FGFs, FGFRs and HSGAGs. The alternative splice isoforms of FGFRs are generally tissue specific: the b isoform is usually expressed in epithelial tissue, whereas the c isoform is usually expressed in mesenchymal tissue23. Ligands are produced in either epithelial or mesenchymal tissue and generally activate receptors of the opposite tissue specificity: in normal physiology, a ligand produced in the epithelium will activate a mesenchymal receptor and vice versa. Several ligands, including FGF1 in particular, pose an exception to this general understanding by promiscuously binding to both b and c isoforms of certain FGFRs. Pathological states can result from a breakdown in binding specificity, as is common in cancers in which FGFs are overexpressed24. Structural studies of FGF1, FGF2, FGF8 and FGF10 with their cognate FGFRs show that sequence diversity at FGF N termini, variation in β1 strand length (FIG. 1b) and the alternatively spliced regions in D3 dictate their binding specificities (FIG. 2b, c).

So it's rather complex. Differences in FGF function are at least in part due to small biochemical differences that may give them differential affinity for different FGFRs, which then go on to transmit the FGF signals down the line. But at the same time the FGFs/FGFRs are expressed in different tissues, meaning that they may have relatively narrow spheres of influence.
If you look here you will see that different FGFs actually have relatively low similarity at the amino acid sequence level, and in some cases quite significant differences in gene structure (though they don't talk about 2 and 5 specifically). One notable difference there:

Most FGFs (FGFs 3-8, 10, 15, 17-19, and 21-23) have amino-terminal signal peptides and are readily secreted from cells. FGFs 9, 16 and 20 lack an obvious amino-terminal signal peptide but are nevertheless secreted [25,26,27]. FGF1 and FGF2 also lack signal sequences, but, unlike FGF9, are not secreted; they can, however, be found on the cell surface and within the extracellular matrix.

For some work on this topic specifically targeted towards FGF2 and FGF5, you can see this paper, which has this table about the location of FGF expression in follicle cells, showing that they are expressed in different places:

apologies to people with screen readers, I didn't have the motivation to copy it out into text. Here is a summary figure that they give: