Tow Law went nap at Chester-le-Street to strengthen their chances of the runner-up spot.
Brian Wake, who recently returned to the club after a spell at Carlisle, led the way with two of the goals, and manager Graeme Forster said; "Brian is slowly getting back to the form he showed with us before he moved to Carlisle.
"But we must keep it going - there's still a lot of hard work to do."
Wake opened the scoring after 36 minutes when he played a 1-2 with Marc Eccles and fired in at the near post, then he got the second in a goalmouth scramble. Kraig Wilkinson scored the third from an Eccles cross before the break, then Andy Hurst volleyed in from the edge of the box after a corner was cleared to him.
Eccles volleyed the goal of the game from an acute angle for the fifth, before Andy Blower pulled a late goal back.
Lawyers are four points behind Dunston who defeated Thornaby 1-0 at Federation Park.
However, Thornaby keeper Nick Bates nearly saved a point for his side, because he stopped an early penalty by Andy Fletcher, and made several other good saves.
But he was finally beaten near the end, when Fletcher scored his 38th goal of the season from a Nicky Scaife cross. Thornaby are now six points adrift of safety, with just four games left.
West Auckland's hopes of finishing second have almost disappeared after they were beaten 2-0 at home by Billingham Town, the visitors' second away win in three days.
Paul Rowntree set up Andy Swalwell to lob West keeper Barry Poskett after 24 minutes, then George Woodhouse ran through to score the second after 55 minutes.
Billingham Synthonia maintained their recent goal scoring form with a 4-1 home win over Brandon.
Lee Flanagan is lose to the 40 goal mark for the season after he opened the scoring from a Dave O'Gorman cross, then midway through the half Dean McGee fired the second.
David Wells raced away for the third just on half time, and on the hour Andy Harbron headed in a Sean O'Brien cross.
Brandon grabbed a late consolation through Steve Huggins.
Washington picked up a valuable three points at home to Peterlee.
Tony Gibson fired them into the lead in the opening minutes, but despite having most of the game, they didn't feel safe until the last ten minutes, when Steve Burns scored from the edge of the box.
Washington are now seven points clear of the relegation zone.
Consett have slipped back into trouble after they were beaten 2-0 at home by Jarrow Roofing, who are now virtually safe.
Consett defender Jeff Sugden put a Craig Nelson cross into his own goal after 12 minutes, but after strong Consett pressure, Nelson missed a penalty following a foul, Consett keeper James Platten saving.
And Jarrow made sure of the points when Paul Chow fire home near the end.
Morpeth are still third bottom, four points adrift of the others, after they lost 3-0 at Guisborough.
They didn't help themselves by having defender Warren Dawson sent off for a professional foul, and another defender, Kevin Harmison, dismissed for violent conduct.
Simon Kasonali converted a penalty for Harmison's indiscretion after 36 minutes, then Thomas Jones volleyed a second on the hour.
Michael Tod wrapped up the points with a powerful strike.
Ashington are still in trouble after they lost 4-0 at FA Vase finalists Whitley Bay.
Mike Fenwick set up Steve Cuggy to put Whitley into the lead after just six minutes, and Andy Bowes cracked in the second from a corner after 36 minutes. Cuggy got the third with a diving header from Jon Sunderland's cross before half time, and it was all over after 49 minutes when Andy Dugdale fired the fourth.
Newcastle Blue Star are fifth from bottom after they drew 2-2 with Durham City, although they were two goals down at one stage. Tony Healer scored from a Stuart Brightwell free kick after 23 minutes, then new signing Ian McQuaid pounced on a mistake in the Star defence to beat Paul Bennett in the Star goal.
Ross Greenhill pulled a goal back from the spot after a push in the area, then Andy Cunningham levelled following a good run down the right wing.
In the second division, leaders Esh Winning are now eight points clear after they strolled to a 5-0 home win over Northallerton, but they couldn't relax until the second half, when they scored four times.
Only two points cover the next four clubs.
Third placed Easington kept their promotion hopes alive when they beat Penrith, one place above them, with a 14th minute goal by Tony Hanson from a Craig Price pass. Penrith and Easington are now level on points, but Penrith have a better goal difference.
Shildon are a point behind them after they won 4-1 at Alnwick. Brian Fairhurst, Nigel Bolton (2) and Danny Richmond scored, all of them set up by John Outhwaite.
Prudhoe are in fifth place after they beat Evenwood 5-1, with Marc Nash scoring a hat trick.
Washington Nissan keeper Steve Watson was amongst the scorers in his side's 8-3 win at Willington, after he was forced to play out because of injuries. Adam Johnson scored a hat trick.
A late goal from David Southern gave Crook the points at Murton.
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