Grainger, 40, and Thornley, 28, re-established their partnership in the double scull after missing out on GB's women's eight for the Rio Olympics.
The duo began Sunday's race positively but faded in the closing stages.
Overall it was a positive regatta for the British team, who won two golds, three silvers and three bronze medals.
Grainger and Thornley had their partnership dissolved in May and were given the opportunity to be considered for the eight.
However, they were not among the 43 rowers named in the Team GB squad on 9 June.
British Rowing performance director Sir David Tanner said earlier this month it was his "confident intention" to get them back into the doubles boat for Rio.
Earlier in Poznan, Britons Helen Glover and Heather Stanning saw off a late surge from New Zealand duo Genevieve Behrent and Rebecca Scown to retain their women's pair's title in a new World Cup best time of six minutes 52.79 seconds.
"We didn't want a race with all the bells and whistles today and we've been training pretty heavily coming into Poznan", said Glover.  'Over the next few weeks is when we will add those bells and whistles".
Alex Gregory, Mohamed Sbihi, George Nash and Constantine Louloudis won gold for Britain in the men's four.
Britain's former Olympic champion James Cracknell told BBC Sport that Grainger and Thornley had "a lot to do" before Rio.
"I don't know where Katherine and Vicky's heads are at the moment," he said.
"They haven't been rowing together a lot in the double scull and this performance is perhaps just a reflection of where they are at.
"It's not such a bad race given that they haven't spent that much time rowing together.
"Over the next five weeks they need to get their boat speed up to be able rattle crews if they want to get on the podium in Rio."
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London Olympic gold medallist Katherine Grainger and Vicky Thornley finished fifth in the women's double scull final at the World Rowing Cup in Poznan.