In D&D 5th Edition, there is a status effect called Exhaustion, which is measured in six levels. Level 5 Exhaustion reduces the speed of a creature to 0.
$$
\begin{array}{|c|c|}
\hline
\textbf{Level} & \textbf{Effect} \\
\hline
\text{1} & \text{Disadvantage on ability checks} \\
\hline
\text{2} & \text{Speed halved} \\
\hline
\text{3} & \text{Disadvantage on attack rolls and saving throws} \\
\hline
\text{4} & \text{Hit point maximum halved} \\
\hline
\text{5} & \text{Speed reduced to 0} \\
\hline
\text{6} & \text{Death} \\
\hline
\end{array}
$$
– PHB 291
There are two other conditions that have a similar effect to this, Grappled and Restrained.
A grappled creature's speed becomes 0, and it can't benefit from any bonus to its speed. – (PHB, p. 290)
A restrained creature's speed becomes 0, and it can't benefit from any bonus to its speed. – (PHBl, p. 292)
In addition, there are spells such as Longstrider, which increase movement speed by a fixed amount (10 feet for Longstrider).
Are bonuses to speed negated by having level 5 exhaustion or can that creature freely move when under an effect that increases its speed?
Best Answer
An exhausted creature can benefit from a bonus to its speed.
A condition does only what it says. The grappled and restrained conditions, as you cited them, state explicitly that the creature can't benefit from any bonus to its speed, but the exhaustion condition states no such thing, nor is there a general rule prohibiting the benefit of bonuses to speed when a creature's speed is reduced to 0.
Specific beats general, so a spell like longstrider would supersede the more general exhaustion condition (on the assumption that one spell out of hundreds is more specific than one common condition out of about a dozen). Otherwise, if that were not the intended precedence, then the grappled and restrained conditions would not even need to state the exception.
This is upheld by Jeremy Crawford, lead rules designer for 5e: "Having 5 levels of exhaustion reduces your speed to 0, but it doesn't prevent bonuses to speed from applying to you." (Source)
This is not surprising if you consider each condition thematically: grappled and restrained represent external factors locking a creature in place to restrict their ability to move (and gaining a bonus to speed would not circumvent that restriction), whereas exhaustion represents the creature's fatigue robbing them of the energy or gumption to move (but gaining a bonus to speed, likely via magic, could overcome that by effectively energizing or motivating them).