Can a creature who is exhausted benefit from bonuses to speed?

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?