Relay driver
A transistor will do what you want ...
I reckon a BC109 (or BC107 or BC108 or BC184) will do the job, they can all cope with 100mA or more.
The resistor is to limit the base current to a safe value (or you could cremate the transistor's B-E junction).
To find a value you need the transistor's hfe (between 125 and 520 for those I listed), this is the gain. You want 75mA out so you must put at least 75/125 mA in to ensure the transistor is turned fully on and so not wasting power as heat.
0.6mA in to the base when the TTL is giving 5v out (and the transistor is forward biassed and therefore dropping 0.6v (ish)). So there is 4.4v across the resistor.
Ohm's law says V=I*R so R=V/I
R= 4.4v / 0.6mA = 7.3kOhms. ###BUT### this is the MINIMUM current for the transistor, a smaller resistor will be fine, all the transistors will cope with 5v EBO, we are calculating at 0.6v.
Try a 1k or a 3k3 resistor !!! (yes, we really do work things out like this !)