Lakshmanan, fresh from winning a gold in the 3,000m event at the Asian Indoor Games in Ashgabat, Turkmenistan, clocked a time of 14 minutes, 4.21 seconds to emerge winner.
Abhishek Pal of Railways came in second, clocking a time of 14 minute 8.38 seconds. Mann Singh of Services took the bronze with a time of 14:08.87.
It was way below Lakshmanan's personal best (of 13:35.69), which he achieved during the Worlds in London.
Incidentally, Surya is the daughter of Lakshmanan's long-time coach S Loganathan.
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In the men's shot put, Tejinder Pal Singh of Services pipped former national record holder Om Prakash Singh to the gold by hurling the iron ball to 18.86 metres.
Tejinder sealed the first place with his final throw after trailing Om Prakash for most part of the competition.
Railways' Jasdeep Singh claimed the bronze medal in the event.
Davinder Singh Kang, who reached the final round of men's javelin throw in the World Athletics Championship in London last month, qualified for the final here.
The men's long jump saw two athletes from the host state Tamil Nadu qualify for tomorrow's final.
Results (All finals):
Men: 5,000m: 1. G Lakshmanan (Services) 14:04.21; 2. Abhishek Pal (Railways) 14:08.38; 3. Mann Singh (Services) 14:08.87.
Shot Put: 1 Tejinder Pal Toor (Services) 18.86m; 2. Om Prakash Singh (ONGC) 18.80m; 3. Jasdeep Singh (Railways) 18.51m.
Women: 5,000m: 1. L Suriya (Railways) 16:02.85; 2. Chinta Yadav (Railways) 16:40.45; 3. Saigeeta Naik (All-India Police) 16:53.97.