For IUPAC nomenclature, does the number of multiple bonds take precedence over the chain length? I've received a few mixed answers to this question. Some sources say when determining the parent chain for unsaturated hydrocarbons, the longest chain should be considered before the chain with the most multiple bonds, for example:
https://www.acdlabs.com/iupac/nomenclature/79/r79_933.htm
While others say what appears to be the opposite, such as this excerpt from Wikipedia:

The steps for naming an organic compound are: 
Identification of the parent hydrocarbon chain. This chain must obey the following rules, in order of precedence:

It should have the maximum number of substituents or branches cited as prefixes.
It should have the maximum number of substituents of the suffix functional group. By suffix, it is meant that the parent functional group should have a suffix, unlike halogen substituents. If more than one functional group is present, the one with highest precedence should be used.
It should have the maximum length.
It should have the maximum number of multiple bonds.
It should have the maximum number of single bonds.


Would be great if I were to receive clarification regarding this.
According to the new recommendations of IUPAC nomenclature rules, when choosing the senior parent structure, you have to first consider the senior parent structure, which has the maximum number of substituents corresponding to the principal characteristic group or senior parent hydride in accord with the seniority of classes. Then, if there is a choice, choose the principal chain, which has the greater number of skeletal atoms. Next in order is the chain, which has the greater number of multiple bonds, and then has the greater number of double bonds (This is according to Blue Book in 2013, which was displayed in 5 steps you have mentioned from Wikipedia).
Note that the new IUPAC recommendations (Blue Book in 2013) on order of chain length and number of multiple bonds have been changed (You can find more details here and here):

In acyclic parent structures the order of seniority between unsaturation and length of chain given in earlier recommendations is reversed. Thus, the first criterion to be considered in choosing a preferred parent acyclic chain is the length of the chain; unsaturation is now the second.

For example consider following structures:

In all first three structures, the longest chain has chosen over the multiple bonds (the old names are in orange). In the typical case, the principle group is $\ce{-CHO}$ and hence hence to hexanal is the principal structure which has $\ce{-OH}$ substituent and longest chain. Thus, the name is 2-ethynyl-5-hydroxyhexanal.