No, depending on the total volume of liquid in your shot the losses will be extremely minimal. If you want to be unnecessarily niggardly with your shot, then you can flush a little extra water through the filter to wash it out. But the diiamorphine will be dissolved, the filter won't "catch" it, the only bit you will lose is from moisture still in the filter which assuming your shot is say 30 units may amount to ~1%. Maybe start with diamorphine dissolved in 20 units of saline, then just wash it out wiith 10 units of plain saline.(although I promise you this isn't really necessary, it will just be for peace of mind)
Is this pharmaceutical diamorphine? 5mg is a tiny dose, I am assuming you are opiate naive? Are you really sure you want to be using needles? Maybe just snort it, I promise you the rush, while enjoyable, isn't worth it. It definitely isn't what movies and the media has made it out to be, the best parts of heroin are in the hours after dosing, not the 15 seconds after taking a shot. In fact, the most enjoyable thing about a shot of heroin is how quickly it makes your withdrawals go away, and most of the look of pleasure on an addicts face is from the relief it brings, not the rush.