Having loaded and over loaded .38 Special rounds for decades, I suggest one use a slower burning powder for heavier loads. Like +P type stuff.
I'm looking at the Hodgdon 2021 Annual Manual as I type. In the .38 Special +p listings, HP-38 is shown as 4.6 grains as maximum.
In Hodgdon #26 (book format) the maximum load of 5.2 grains of HP-38 is shown. That book (and information) has a publishing date of 1992. Since then, pressure testing has been advanced and loads that used to be used are now determined to be above the allowed industry (SAAMI) standards of pressure.
Important note: Exceeding the maximum charge will probably NOT result in a first shot catastrophic failure (blowing up and bits of what used to be a revolver and casing falling from the sky). But it will wear out the firearm sooner; probably in the realm of stretching the top strap of a revolver, ending in excessive end play. And it could blow up completely on the 21st or 22nd shot.
That same 2021 Hodgdon manual lists at least three other loadings for the same caliber and bullet going faster than the one with which you're experimenting, some resulting in lower pressures.
Do be careful, old boy.