The Identity command solves a system containing one or more identities. The difference between calling Identity and calling solve on a system of identities, is that Identity does only enough processing to remove the identities before attempting to solve the system.  The solve command does much more processing and so may return more complete answers for a system with a mix of identities and other equations or inequations.

$\mathrm{SolveTools}:-\mathrm{Identity}\left(\left\{\mathrm{identity}\left(t^z-x^t+5^t=\frac{1}{t}\,t\right)\right\}\,\varnothing \,\left\{x\,z\right\}\right)$

$\left[\left\{x=5\,z=\mathrm{-1}\right\}\right]$

$\mathrm{SolveTools}:-\mathrm{Identity}\left(\left\{\mathrm{identity}\left(\frac{y}{x}=a{\left(x+c\right)}^b\,x\right)\right\}\,\varnothing \,\left\{a\,b\,c\right\}\right)$

$\left[\left\{a=y\,b=\mathrm{-1}\,c=0\right\}\right]$