The other easy option you can do on the supply line to the shower is install a mixing valve that way you can control the maximum water temp to the shower while letting the rest of the house run hotter water.
That said you may just need to replace the cartridges on your shower would be easier first try and cheaper too. As a general rule for safety sake your hot water tank should be kept above 140f it kills stuff like legionairs in the water.
Since most of the legionnaires' bacteria can also reside in your aerators, shower heads, etc... in your system, keeping the water at 140 degrees at the heater is not guarantee that they will be killed at these areas as the water will cool down in transit. Further, adding in a mixing valve to cool down 140 degree to 120 degree or lower at the shower head or tub spout would defeat the 140* water. In short, I'd set my heater to 120* and reduce heating costs, risk of scalding. The pdf I referenced said 120* will kill 90% of bacteria in a few hours exposure (a bit slower than the 140* which also is about 90% kill rate) so you aren't losing much.
How much pipe between heater and shower? It can take a while for all the cold water in the hot water supply piping to exit the shower head before the hot water that follows it comes out the shower head (depending on run of piping, shower head flow rate, ambient temperature, etc).
Run the hot only side of the shower until you think it is not getting hotter with your hand. Measure the temperature. Wait another 5 minutes and measure the temp of the water again. Is it much different?
When I turn it on yes I let it get hot first. The thing is it never happens in the other shower only this one. I would say there is maybe 30-40ft of pipe between the heater and shower and maybe only another 30ft to the other shower. Could it be the hot water valve in the shower heats up after 5 minutes or so then opens up more?
"...then it just gets scalding hot after 5 minutes or so"
If the valve is one of those temperature maintaining ones (meant to prevent scalding or freezing during a shower) the mix valve may be messed up. I'm sure a pro can advise on how to fix or google it.
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