I always look up to £1k over budget, higher if budget is over £10k, that way you will not miss one that is £250 over budget or one that drops in price into your budget after being on the market a while, most people build in some wriggle room, 10% at least, getting tack included is useful for a first time buyer but it should be a bargaining point and not expected unless it is stated in the ad.
I usually try and sell with tack, basic rugs if the horse is genuinely outgrown/ owner giving up but if they are moving onto something similar in size they may want to keep most of the stuff in case it fits the new one, so don't let not coming with tack be a deal breaker even if it means a bit of haggling to get something within budget, 5k is reasonable so there should be a few to look at.