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We have observed 7 new transits of the `hot Jupiter WASP-5b using a 61 cm telescope located in New Zealand, in order to search for transit timing variations (TTVs) which can be induced by additional bodies existing in the system. When combined with o ther available photometric and radial velocity (RV) data, we find that its transit timings do not match a linear ephemeris; the best fit chi^2 values is 32.2 with 9 degrees of freedom which corresponds to a confidence level of 99.982 % or 3.7 sigma. This result indicates that excess variations of transit timings has been observed, due either to unknown systematic effects or possibly to real TTVs. The TTV amplitude is as large as 50 s, and if this is real, it cannot be explained by other effects than that due to an additional body or bodies. From the RV data, we put an upper limit on the RV amplitude caused by the possible secondary body (planet) as 21 m s^{-1}, which corresponds to its mass of 22-70 M_{Earth} over the orbital period ratio of the two planets from 0.2 to 5.0. From the TTVs data, using the numerical simulations, we place more stringent limits down to 2 M_{Earth} near 1:2 and 2:1 mean motion resonances (MMRs) with WASP-5b at the 3 sigma level, assuming that the two planets are co-planer. We also put an upper limit on excess of Trojan mass as 43 M_{Earth} (3 sigma) using both RV and photometric data. We also find that if the possible secondary planet has non- or a small eccentricity, its orbit would likely be near low-order MMRs. Further follow-up photometric and spectroscopic observations will be required to confirm the reality of the TTV signal, and results such as these will provide important information for the migration mechanisms of planetary systems.
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