Context : The gamma-ray binary LS 5039 and the isolated pulsar PSR J1825 - 1446 were proposed to have been formed in the supernova remnant ( SNR ) G016.8 - 01.1 .

Aims : We aim to obtain the Galactic trajectory of LS 5039 and PSR J1825 - 1446 to find their origin in the Galaxy , and in particular to check their association with SNR G016.8 - 01.1 to restrict their age .

Methods : By means of radio and optical observations we obtained the proper motion and the space velocity of the sources .

Results : The proper motion of PSR J1825 - 1446 corresponds to a transverse space velocity of 690 km s ^ { -1 } at a distance of 5 kpc .
Its Galactic velocity at different distances is not compatible with the expected Galactic rotation .
The velocity and characteristic age of PSR J1825 - 1446 make it incompatible with SNR G016.8 - 01.1 .
There are no clear OB associations or SNRs crossing the past trajectory of PSR J1825 - 1446 .
We estimate the age of the pulsar to be 80–245 kyr , which is compatible with its characteristic age .
The proper motion of LS 5039 is \mu _ { \alpha } \cos \delta = 7.09 and \mu _ { \delta } = -8.82 mas yr ^ { -1 } .
The association of LS 5039 with SNR G016.8 - 01.1 is unlikely , although we can not to discard it .
The system would have had to be formed in the association Ser OB2 ( at 2.0 kpc ) if the age of the system is 1.0–1.2 Myr , or in the association Sct OB3 ( distance 1.5–2 kpc ) for an age of 0.1–0.2 Myr .
If the system were not formed close to Ser OB2 , the pseudo-synchronization of the orbit would be unlikely .

Conclusions : PSR J1825 - 1446 is a high-velocity isolated pulsar ejected from the Galaxy .
The distance to LS 5039 , which needs to be constrained by future astrometric missions such as Gaia , is a key parameter for restricting its origin and age .