A single note with this duration is a triply dotted triplet quarter note:
- triple dotting increases the duration by a factor of 15/8
- notes in a triplet are shortened by a factor of 2/3
- the product of these factors is 5/4
But there are serious problems with this approach:
- it is cumbersome if not impossible to apply triplet shortening to a single note
- doubly and triply dotted notes are not readily comprehended except as one element of a pair (for example, dotted quarter and eighth, doubly dotted quarter and sixteenth, triply dotted quarter and 32nd)
- nobody is going to be able to do all this arithmetic in their heads while they're playing an instrument or singing.
By contrast, reading tied notes is an elementary skill, and if the component values of the tie are chosen carefully, the relationship between the metrical pulse and the note's beginning and end will be clear.
The goal of music notation is not to express pitch and duration in the most efficient way possible, but to communicate with a reader, whether for performance or study.
Since the relationship between rhythm and meter is an important part of that communication, the use of tied notes to represent complex rhythms, especially unfamiliar ones, is a feature, not a bug.
Also see my answer to How to represent 5 eighth-notes as one note?