In this paper, we show that if two non-constant meromorphic functions
f
f
and
g
g
satisfy
E
¯
(
a
j
,
k
,
f
)
=
E
¯
(
a
j
,
k
,
g
)
\overline {E}(a_{j},k,f)=\overline {E}(a_{j},k,g)
for
j
=
1
,
2
,
…
,
5
j=1,2,\dots ,5
, where
a
j
a_{j}
are five distinct small functions with respect to
f
f
and
g
g
, and
k
k
is a positive integer or
∞
\infty
with
k
≥
14
k\geq 14
, then
f
≡
g
f\equiv g
. As a special case this also answers the long-standing problem on uniqueness of meromorphic functions concerning small functions.