Knight and Stob proved that every low
4
_4
Boolean algebra is
0
(
6
)
0^{(6)}
-isomorphic to a computable one. Furthermore, for
n
=
1
,
2
,
3
,
4
n=1,2,3,4
, every low
n
_n
Boolean algebra is
0
(
n
+
2
)
0^{(n+2)}
-isomorphic to a computable one. We show that this is not true for
n
=
5
n=5
: there is a low
5
_5
Boolean algebra that is not
0
(
7
)
0^{(7)}
-isomorphic to any computable Boolean algebra.
It is worth remarking that, because of the machinery developed, the proof uses at most a
0
′
′
0^{\prime \prime }
-priority argument. The technique used to construct this Boolean algebra is new and might be useful in other applications, such as to solve the low
n
_n
Boolean algebra problem either positively or negatively.