Yes, even if all six are 5th cousins, some will share more DNA than you with others and some may not be detected.
Here is a helpful graphic on coefficients of relatedness indicating approximately how much DNA you will share with different types of relatives on average. You can also look at the table under the "Human relationships" section of this "Coefficient of relationship" Wikipedia article
As you can see from this coefficient of relatedness table fourth cousins share about 0.2% of their DNA. 5th cousins will share even less. Then add in the fact that this is only an average (due to an element of random chance involved in how genetics works, some of your 4th cousins will share less than 0.2% of their DNA with you and some will share more.
With such small numbers (0.2% is a very small amount of DNA!) the distinction between 4th cousins, 5th cousins, etc are a lot less reliable statistically. For example, second degree relatives share about 25% of their DNA but some people that are second degree relatives might share a couple percentages more or less than this. So when you are trying to distinguish between 4th and 5th cousins and dealing with partial percentages its a lot less exact because a certain amount of shared DNA could be indicative of several different degrees of relatedness and genealogical records would have to be used to give you the exact degree of relatedness.
See also this helpful answer explaining why one second cousin may share 4% of their DNA with you while another may share 8%.