Unfortunately I haven;t got £5k for you, but a few ideas, you may have already tried?
Why not contact a large pub and promise to come after every match, and give them say a target of at least 20 get togethers, which includes the after match meets etc.
Based upon say 15 people attending, thats a probable spend of £225 a time, more if your all drinkers. So the venue gets an incom ein food and drink of £4500 over the year, with a profit of typically 45% across food and beverage, thats a profit they would make of £2025
Ask them for this amount as sponsorship, they get a few ads etc, and offer them shirt sponsorship for another £2000.
Why would they give you all their profit, Cos its not much of a gamble for them and they would probably get more, and all the extra business it would bring in.
Check with the planners, anyone recently applied for a big project, been refused a project etc, get them involved, and their efforts in the local community wont go un noticed by the planners, use this as your bargaining chip. This would be the most liley shirt sponsor, ne wbuild developer sat on a load of vacant properties, or plots and no buyers, perfect for them, plus as its a write off, these big players find it easy to do deals at this level.
I'm sure there are dozens more, but my two penneth, about the amount I have to donate