It's been a few years since I've had my H5, however I remember that it had a manual focus mode that I used when I was shooting low light or night sky photography and needed infinity focus. The focus selection button on top should give you that option, then you use the control pad to move the on-screen focus bar over to infinity. Remember that sometimes true infinity focus is actually just a hair back from the farthest setting - many cameras actually adjust focus a bit 'beyond' infinity. Without a way to magnify the screen, it may be hard to determine accurate focus, but that should get you pretty close. If you can find a star that's brighter, the H5 has a 'peaking' function in MF mode which will highlight the areas in blue that are in focus to help you get it right. In manual focus mode, you can always find a larger object like the moon to focus on, then recompose and meter off of the area you intend to shoot - the manual focus will stay where you set it so you don't get all the hunting around trying to AF.
Sony DSLR-A68 / Sony 18-250mm / Minolta 50mm F1.7 / Tamron 150-600mm / Minolta 300mm F4 APO
Sony A6300 / 18-55mm F3.5-5.6 / 55-210mm F4-6.3 / 10-18mm F4 / 35mm F1.8 / 16mm F2.8 / FE70-200mm F4 G OSS / FE70-300mm F4.5-5.6 G OSS / via manual adapter, lots of Pentax K mount, Konica K/AR mount, and Leica M mount manual lenses