I realise that this is an old thread, but the OP's request (
short lycra tights with 4"-5" inseams) is timeless!
So, this is a shout-out for Skins brand men's 'Dnamic' short tights (yes, Dnamic not Dynamic). Skins actually offer two lengths of 'short' lycra tights. Terminology varies between sellers; Skins themselves refer to them as 'Dnamic half tights' (the longer) and 'Dnamic shorts' (the shorter, 5" inseam). The latter are intended as a base layer to be worn under regular shorts to stop chafing, but IMO they are just fine to wear without regular shorts over. The material is thick, not flimsy; compression is firm and keeps the bulge under control; the colourways are solid, not pastel.
It's worth bearing in mind that, for any given length of inseam, lycra shorts will end noticeably higher on the thigh than the same length inseam in regular shorts. Because, the crotch of the shorts fits tight against the wearer's crotch with lycra shorts, but hangs an inch or two lower for regular shorts (especially if they have a liner).
I like my Skins Dnamic 5" shorts very much. They end clearly more than halfway up the thigh, but they're not so short as to be seen as hotpants, which for me would be a step too far on the gym floor. The fact that they're solid, not pastel, colours (I have the black/yellow colourway), with a known-brand logo, adds credibility, especially when worn with a matching Skins top. It avoids the impression that I've been rummaging around on discount Chinese-source websites for something skimpy and sexy! As you might have guessed, I enjoy hovering just on that boundary of people wondering (or so I imagine) "is that guy posing in that kit? Or not?"
Actually it looks as if the Dnamic short shorts might have been discontinued - a search for 'Dnamic' at
http://www.skinscompression.com didn't show them. But they can still be sourced, often with substantial discounts, with a bit of googling eg
https://www.sportsshoes.com/product/...ession-shorts/
https://www.jimkiddsports.com.au/pro...-da99050099238
https://www.ebay.co.uk/itm/Skins-Men...AOSwWnRdpsg u
https://www.amazon.co.uk/Skins-DNAmi...1-9&th=1&psc=1