There is a program called Easy strength by Dan John and Pavel Tsatsouline that have you doing each exercise 2 sets x 5 repetitions 5 days a week.
The important part here is to go really easy on each set (hence the name) in order to not accumulate much fatigue.

This program probably works slightly better than a 3 sets x 5 repetitions 3 days a week program. The reason is probably that frequent practice causes more of some not yet understood neural adaptation.  

For most people training 3 x a week is more practical than 5 x a week. 
However for some people such as firefighters, police officers and military personell, high frequency training may be better.
The reason is that with this style of training you are never really badly fatigued in case you eg have to run after a criminal. The same thing may not be so easy the day after 3 or 5 sets of 5 reps almost to failure squats.

Also there is a newer model of stimulus and recovery named the [fitness-fatigue model][1]:
[![enter image description here][2]][2]

In this model you are getting stronger from immediately after your workout.
However the increase in fitness is masked by fatigue so that the performance is worse until you have recovered from the fatigue.
 



 


  [1]: https://medium.com/@SandCResearch/what-is-the-fitness-fatigue-model-6a6ca3274aab
  [2]: https://i.sstatic.net/86ERL.jpg